What Is The Value Of The T Score For A 99% Confidence Interval If We Take A Sample Of Size 10?

If you're simply beginning statistics, you'll probably be finding confidence intervals using the normal distribution (see #3 below). But in reality, virtually conviction intervals are found using the t-distribution (especially if yous are working with small samples). Picket the video for an case:

Confidence interval for a sample

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Contents (Click to Skip to Section)

• What is a Confidence Interval?

How to Find a Conviction Interval by Hand:

1. How to Find a Confidence Interval for a Sample (T-Distribution)
2. How to Find a Confidence Interval for a Sample (Example 2)
3. How to Find a Conviction Interval with the Normal Distribution / Z-Distribution
4. How to Notice a Conviction Interval for a Proportion
5. How to Find a Confidence Interval for Ii Populations (Proportions)

How to Discover a Confidence Interval using Technology:

1. Confidence Interval for the Mean in Excel
2. Conviction Interval on the TI 83: Two Populations;
3. Using the TI 83 to Find a Confidence Interval for Population Proportion, p
4. TI 83 Confidence Interval for the Population Mean
5. Confidence Interval for a Mean on the TI 89
6. Conviction Interval for a Proportion on the TI 89

Explanations and Definitions:

1. The 95% Confidence Interval Explained
2. Disproportionate Confidence Interval
3. 95 Percent Conviction Interval (Function III of Intro to Statistics)
4. What is a Wald CI?
5. Wilson CI

See as well:

Binomial Conviction Intervals.
What is a Z Interval?

What is the Definition of a Confidence Interval?

A confidence interval is how much dubiousness there is with whatever item statistic. Confidence intervals are oft used with a margin of fault. Information technology tells you how confident yous tin can be that the results from a poll or survey reverberate what yous would look to find if information technology were possible to survey the entire population. Conviction intervals are intrinsically connected to conviction levels.

Confidence Intervals vs. Confidence Levels

Confidence levels are expressed as a percentage (for example, a 95% conviction level). It ways that should you repeat an experiment or survey over and over again, 95 percent of the time your results volition match the results you get from a population (in other words, your statistics would exist sound!). Confidence intervals are your results and they are unremarkably numbers. For example, you survey a grouping of pet owners to see how many cans of dog food they purchase a year. You examination your statistic at the 99 percentage confidence level and get a confidence interval of (200,300). That means you think they buy betwixt 200 and 300 cans a yr. You lot're super confident (99% is a very loftier level!) that your results are audio, statistically.

Image: WUSTL.EDU

Real Life Examples of Confidence Intervals

A 2008 Gallup survey found that Tv set ownership may be good for wellbeing. The results from the poll stated that the conviction level was 95% +/-3, which means that if Gallup repeated the poll over and over, using the aforementioned techniques, 95% of the time the results would fall inside the published results. The 95% is the confidence level and the +/-three is called a margin of fault. At the kickoff of the article you'll run into statistics (and bar graphs). At the lesser of the commodity you'll meet the confidence intervals. For example, "For the European data, one can say with 95% confidence that the true population for wellbeing among those without TVs is between four.88 and 5.26." The confidence interval here is "between 4.88 and 5.26".

The U.South. Census Bureau routinely uses confidence levels of ninety% in their surveys. 1 survey of the number of people in poverty in 1995 stated a confidence level of 90% for the statistics "The number of people in poverty in the United States is 35,534,124 to 37,315,094." That means if the Demography Bureau repeated the survey using the aforementioned techniques, ninety percent of the fourth dimension the results would autumn between 35,534,124 and 37,315,094 people in poverty. The stated effigy (35,534,124 to 37,315,094) is the confidence interval.
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Confidence Interval For a Sample: Overview

When you don't know annihilation about a population'southward beliefs (i.due east. y'all're but looking at data for a sample), y'all need to use the t-distribution to discover the confidence interval. That's the vast majority of cases: you unremarkably don't know population parameters, otherwise you wouldn't be looking at statistics!

The confidence interval tells you lot how confident you are in your results. With any survey or experiment, y'all're never 100% sure that your results could be repeated. If y'all're 95% certain, or 98% sure, that'southward usually considered "good enough" in statistics. That percentage of sureness is the confidence interval.

Conviction Interval For a Sample: Steps

Question:

A grouping of 10 foot surgery patients had a hateful weight of 240 pounds. The sample standard deviation was 25 pounds. Find a confidence interval for a sample for the true hateful weight of all foot surgery patients. Find a 95% CI.

Step 1: Subtract 1 from your sample size. 10 – 1 = 9. This gives you lot degrees of freedom, which y'all'll need in step 3.

Step 2: Subtract the confidence level from 1, then carve up past ii.
(one – .95) / 2 = .025

Pace 3: Look upward your answers to step 1 and 2 in the t-distribution tabular array. For ix degrees of freedom (df) and α = 0.025, my result is 2.262.

df	α = 0.one	0.05	0.025	0.01	0.005	0.001	0.0005
∞	tα=1.282	1.645	1.960	2.326	2.576	iii.091	iii.291
1	3.078	vi.314	12.706	31.821	63.656	318.289	636.578
2	1.886	ii.920	4.303	6.965	9.925	22.328	31.600
iii	ane.638	two.353	3.182	iv.541	5.841	10.214	12.924
4	1.533	two.132	two.776	3.747	4.604	7.173	8.610
v	1.476	2.015	2.571	iii.365	four.032	five.894	6.869
vi	1.440	1.943	2.447	3.143	iii.707	5.208	five.959
7	i.415	one.895	2.365	ii.998	3.499	4.785	5.408
eight	1.397	1.860	2.306	2.896	3.355	4.501	5.041
9	1.383	ane.833	2.262

Step 4: Divide your sample standard divergence by the square root of your sample size.
25 / √(10) = 7.90569415

Step 5: Multiply step 3 by stride four.
2.262 × 7.90569415 = 17.8826802

Step half dozen: For the lower cease of the range , subtract pace five from the sample mean.
240 – 17.8826802 = 222.117

Step 7: For the upper stop of the range, add step 5 to the sample hateful.
240 + 17.8826802 = 257.883

That's how to observe the confidence interval for a sample!

Like the explanation on how to discover a confidence interval? Cheque out our statistics how-to book, with a how-to for every unproblematic statistics problem type.

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How to Find a Confidence Interval Example 2 (minor sample)

Watch the video for an example:

How to find a confidence interval with a t distribution

Tin't see the video? Click here.

If you have one small set of data (under 30 items), you lot'll want to employ the t-distribution instead of the normal distribution to construct your confidence interval.

The formula for constructing a CI with the t-distribution.

Case problem: Construct a 98% Conviction Interval based on the post-obit data: 45, 55, 67, 45, 68, 79, 98, 87, 84, 82.

Step 1: Find the mean, μ and standard deviation, σ for the information.
σ: xviii.172.
μ: 71
Set these numbers aside for a moment.

Step 2: Decrease 1 from your sample size to discover the degrees of liberty (df). Nosotros accept x numbers listed, so our sample size is 10, so our df = 9. Prepare this number aside for a moment.

Step 3: Decrease the conviction level from 1, then divide past two. This is your alpha level.
(1 – .98) / 2 = .01

Pace four: Look up df (Step 2) and α (Step 3) in the t-distribution table. For df = 9 and α = .01, the table gives the states two.821.

Degrees of liberty in the left column of the t distribution tabular array.

Step 5: Divide your std dev (step 1) by the foursquare root of your sample size.
18.172 / √(10) = 5.75

Step 6: : Multiply pace 4 by footstep five.
2.821 × 5.75 = sixteen.22075

Step seven: For the lower end of the range , decrease step half dozen from the mean (Step one).
71 – 16.22075 = 54.77925

Step viii: For the upper end of the range, add pace half-dozen to the hateful (Step 1).
71 + xvi.22075 = 87.22075

That's how to find a confidence interval using the t-distribution!
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Confidence Interval with the Normal Distribution / Z-Distribution

Lookout the video for an example:

How to notice a confidence interval with a z distribution

Tin't encounter the video? Click here.

If you don't know your population mean (μ) simply you practice know the standard deviation (σ), you can find a confidence interval for the population mean, with the formula:
x̄ ± z* σ / (√n),

Case trouble: Construct a 95 % confidence interval an experiment that found the sample mean temperature for a certain metropolis in August was 101.82, with a population standard departure of 1.ii. There were 6 samples in this experiment.

Step 1: Decrease the confidence level (Given equally 95 percent in the question) from i and so split up the result by ii. This is your alpha level, which represents the surface area in one tail.
(1 – .95) / 2 = .025

Stride ii: Subtract your result from Pace one from 1 and so expect that area up in the middle of the z-table to get the z-score:

1. one – 0.025 = 0.975
2. z score = one.96.

Step 3: Plug the numbers into the second part of the formula and solve:
z* σ / (√n)
= ane.96 * ane.2/√(half dozen)
= i.96 * 0.49
= 0.96

Step iv: For the lower end of the range, subtract step 3 from the mean.
101.82 – 0.96 = 100.86

Step 5: For the upper end of the range, add step 3 to the  hateful.
101.82 + 0.96 = 102.78.

The CI is (100.86,102.78)

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How to Find a Confidence Interval for a Proportion: Overview

Watch the video for an instance of finding a conviction interval for population proportion of successes (and failures):

Confidence Interval for Population Proportion of Successes

Tin't see the video? Click hither.

When we talk nigh a confidence interval (CI), we're dealing with information. For case, allow's say the manager for that job you applied for told you he would become dorsum with y'all in a "couple of days." A couple of days could mean two. Or three. Or there might be a paperwork backlog and information technology could exist a calendar week. It definitely doesn't mean in an hour. And then your CI would probably be between two and 4 days.

Perhaps the trickiest part of CIs is recognizing the various parts needed for the formula, like z a/two. This section breaks everything down into unproblematic steps and shows you how to find a conviction interval for population proportions.

How to Discover a Conviction Interval for a Proportion: Steps

Watch the video for another example:

How to find a confidence interval for a proportion

Tin can't run into the video? Click hither.

Question: 510 people applied to the Bachelor's in Uncomplicated Education program at Florida State College. Of those applicants, 57 were men. Detect the 90% CI of the true proportion of men who applied to the program.

Step 1: Read the question carefully and figure out the following variables:

• Observe z α/two. You don't have to look this up in the z-table every time, you tin discover mutual ones in this tabular array:
  

  Co-ordinate to the table, for a 90% CI, z α/two = 1.645.

• p-hat: Divide the proportion given (i.eastward. the smaller number)past the sample size. 57/510 = 0.112
• q-hat: To find q-hat, subtract p-hat (from straight above) from i. This gives: 1 – 0.112 = 0.888

Step 2: Multiply p-hat by q-hat (from Step 1).
0.112 x 0.888 = 0.099456

Step 3: Divide footstep ii past the sample size.
0.099456 / 510 = 0.000195011765

Stride 4: Accept the square root of step 3:
sqrt(0.000195011765) = 0.0139646613

Pace 5: Multiply step four past z _a/2 :
0.0139646613 x ane.645 = 0.023.

Step 6: : For the lower percentage, subtract step 5 from p-lid.
0.112 – 0.023 =  0.089 = viii.9%.

Stride 7: For the upper percentage, add together pace v to p-hat.
0.112 + 0.023 =  13.5%.

This next method involves plugging in numbers into the actual formula. You'll get the aforementioned results if yous use the "formula free" method above or if you lot use the steps below.

Confidence intervals for a proportion are calculated using the following formula:

The formula might look daunting, merely all you really need are two pieces of information: the z-score and the P-hat. You lot should be familiar with looking up z-scores from previous sections on the normal distribution (if you need a refresher, exist sure to watch the in a higher place video) and P-hat is just dividing the number of events by the number of trials. One time you've figured those two items out, the residuum is bones math.

Confidence Interval for a Proportion Instance ii: Steps

Example question: Calculate a 95% conviction interval for the true population proportion using the following data:
Number of trials(n) = 160
Number of events (10) = 24

Step 1: Divide your confidence level by 2: .95/2 = 0.475.

Step two: Look upwards the value you calculated in Step 1 in the z-table and find the respective z-value. The z-value that has an expanse of .475 is one.96.

Footstep 3: Divide the number of events by the number of trials to get the "P-hat" value: 24/160 = 0.15.

Step four: Plug your numbers into the formula and solve:

1. 0.15 ± (one.96) √ ((0.15(1 – 0.15) / 160))=
2. 0.fifteen ± (1.96) √ ((0.15(0.85)/160))=
3. 0.15 ± (1.96) √ ((0.1275)/160))=
4. 0.xv ± (one.96) √ (0.000796875)=
5. 0.15 ± (1.96) 0.0282289744765905=
6. 0.fifteen ± 0.0553 =
7. 0.15 – 0.0553 = 0.0947 <--this is your lower confidence interval for a proportion
8. 0.15 + 0.0553 = 0.2053 <--this is your upper conviction interval for a proportion

Your answer can be expressed as: (0.0947,0.ii.053).
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How to Find a Confidence Interval for 2 Populations (Proportions)

Finding conviction intervals for 2 populations tin look daunting, especially when you have a wait at the ugly equation below.

Information technology looks a lot worse than information technology is, considering the right side of the equation is actually a echo of the left! Finding confidence intervals for 2 populations can be broken down to an like shooting fish in a barrel three steps.

Example question: A study revealed that 65% of men surveyed supported the war in Transitional islamic state of afghanistan and 33% of women supported the war. If 100 men and 75 women were surveyed, find the xc% conviction interval for the information's truthful divergence in proportions.

Pace one: Detect the following variables from the information given in the question:
n_i (population 1)=100

Phat1 (population one, positive response): 65% or 0.65
Qhat1 (population one, negative response): 35% or 0.35
n₂(population 2)=75
Phat2 (population 2, positive response): 33% or 0.33
Qhat2 (population 2, negative response): 67% or 0.67

Step 2: Find z _α/2
(If you've forgotten how to find α/2, see the directions in: How to Discover a Confidence Interval for a Proportion above)
z_α/2=0.13

Step 3: Enter your data into the following formula and solve:

If formulas scare yous, here'south the footstep-past-pace to solve the equation (refer dorsum to step i for the variables):

1. multiply phat1 and qhat1 together (.65 x .35 = .2275)
2. divide your answer to (1) past north₁. Set this number aside. (.2275 x 100=.00275)
3. multiply phat2 and qhat2 together (.33 x .67=.2211).
4. split your answer to (3) by northward_{2 (.2211/75=.002948)}.
5. Add (3) and (4) together (.00275 + .002948=.005698)
6. Accept the square root of (5): (sqrt.005698=.075485)
7. Multiply (vi) by z_α/2 establish in Pace 2. (.075485 x 0.13=.0098). Prepare this number aside.
8. Subtract phat2 from phat1 (.65-.33=.32).
9. Subtract (8) from (7) to get the left limit (.32-0.0098 = 31.9902)
10. Add (7) to (viii) to get the right limit (.32+.0.0098=32.0098)

That'due south information technology!
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Confidence Interval for the Hateful in Excel

Watch the video for an example:

Confidence interval for the mean in Excel

Tin't see the video? Click here.

How to Find a Conviction Interval for the Mean in Excel: Overview

CI for the mean formula.

A confidence interval for the mean is a fashion of estimating the true population mean. Instead of a single number for the hateful, a confidence interval gives you a lower estimate and an upper estimate. For example, instead of "6" as the mean you might get {v,7}, where 5 is the lower estimate and vii is the upper. The narrower the estimate, the more than precise your approximate is. The equations involved in statistics often involve a lot of small calculations (such as summation), plus you lot would also need to calculate the margin of error and the mean of the sample. It's very easy for errors to slip in if you summate the confidence interval by paw. However, Excel can calculate the mean of the sample, the margin or error and confidence interval for the mean for you. All you take to do is provide the data —which for this technique must be a sample greater than about 30 to give an accurate conviction interval for the mean.

How to Detect a Conviction Interval for the Hateful in Excel: Steps

Instance problem:Calculate the 95 percent confidence interval for the mean in Excel using the following sample information: 2, 5, 78, 45, 69, 100, 34, 486, 34, 36, 85, 37, 37, 84, 94, 100, 567, 436, 374, 373, 664, 45, 68, 35, 56, 67, 87, 101, 356, 56, 31.
Pace 1: Blazon your data into a single column in Excel. For this example, type the information into cells A1:A31.

Footstep 2: Click the "Data" tab, and then click "Data Analysis," then click "Descriptive Statistics" and "OK." If you don't see Data Analysis, load the Excel information analysis toolpak.

Pace 3: Enter your input range into the Input Range box. For this example, your input range is "A1:A31".

Stride 4: Type an output range into the Output Range box. This is where y'all want your answer to appear. For example, type "B1."

Footstep five: Click the "Summary Statistics" check box then place your chosen confidence level into the 'Confidence Level for Hateful' check box. For this case, type "95".

Step v: Click "OK."Microsoft Excel will return the confidence interval for the mean and the margin of error for your information. For this sample, the hateful (Xbar) is 149.742 and the margin of error is 66.9367. So the mean has a lower limit of 149.742-66.936 and an upper limit of 149.742+66.936.

That'south it!

Warning: A 99 percent conviction interval doesn't mean that there's a 99 percent probability that the calculated interval has the bodily mean. Your sample is either going to comprise the bodily mean, or it isn't. Over the long-term, if you ran tests on many, many samples, there is a 99 percentage probability that the calculated intervals would comprise the truthful hateful.
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TI 83 Conviction Interval:Two Populations

Statistics about two populations is incredibly important for a diversity of inquiry areas. For example, if there's a new drug being tested for diabetes, researchers might exist interested in comparing the mean blood glucose level of the new drug takers versus the mean blood glucose level of a control grouping. The confidence interval(CI) for the difference between the two population means is used to aid researchers in questions such as these.

The TI 83 allows you lot to find a CI for the difference between two means in a matter of a few keystrokes.

Example problem: Detect a 98% CI for the departure in ways for 2 usually distributed populations with the following characteristics:

x _i = 88.five
σ_i = xv.viii
n_one = 38

x _two = 74.five
σ₂= 12.3
northward₂ = 48

Step 1: Press STAT, then use the correct pointer key to highlight TESTS.

Pace 2: Printing 9 to select 2-SampZInt….

Pace iii: Correct pointer to Stats and so press ENTER. Enter the values from the trouble into the appropriate rows, using the downwards arrow to switch between rows equally yous complete them.

Step 4 : Use the downwardly pointer to select Summate and then press ENTER.

The answer displayed is (half-dozen.7467, 21.253). We're 98% sure that the difference between the two means is between 6.7467 and 21.253.

That'south it!

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How to Find a Confidence Interval for Population Proportion, p on the TI 83

Watch the video for the steps:

TI 83 Confidence Interval Population Proportion

Tin can't encounter the video? Click here.

Instance problem: A recent poll shows that 879 of 1412 Americans have had at least 1 caffeinated beverage in the concluding calendar week. Construct a 90% confidence interval for p, the true population proportion.

Notation:

• "10" is the number of successes and must be a whole number. Successes in this question is how many Americans have had at least one caffeinated beverage (879). If you lot are given p̂ instead (the sample proportion), multiply p̂ past n to get x (because 10=n* p̂).
• "north" is the number of trials.

Step one: Press STAT.

Step two: Right arrow over to "TESTS."

Footstep 3: Pointer downward to "A:1–PropZInt…" and then press ENTER.

Step four: Enter your x-value: 879.

Step 5: Arrow downwardly and and so enter your due north value: 1412.

Step 6 : Pointer down to "C-Level" and enter .90. This is your confidence level and must exist entered every bit a decimal.

Step 7 : Pointer downward to calculate and press ENTER. The calculator volition render the range (.6013, .64374)

That means the 98 per centum CI for the population proportion is between 0.6013 and .64374.

Tip: Instead of arrowing downward to select A:1–PropZInt…, press Alpha and MATH instead.
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How to Detect a Confidence Interval on the TI 83 for the Population Hateful

If you don't know how to enter data into a list, yous can find the information in this article on TI 83 cumulative frequency tables.

Watch the video for the steps:

TI 83 Confidence Interval Population Mean

Can't come across the video? Click here.

Example trouble: xl items are sampled from a normally distributed population with a sample mean x̄ of 22.1 and a population standard deviation(σ) of 12.8. Construct a 98% conviction interval for the true population hateful.

Stride ane : Printing STAT, then correct arrow over to "TESTS."

Step 2 : Press vii for "Z Interval."

Step 3 : Arrow over to "Stats" on the "Inpt" line and press ENTER to highlight and movement to the next line, σ.

Step four : Enter 12.8, then arrow down to x̄.

Footstep v : Enter 22.1, and so pointer downwardly to "n."

Stride 6 : Enter 40, and then arrow down to "C-Level."

Step vii : Enter .98. Arrow down to "calculate" and and then press ENTER. The calculator will requite you the result of (17.392, 26.808) meaning that your 98% confidence interval is 17.392 to 26.808. This is the same as:

17.392 > μ > 26.808

That's how to find a Conviction Interval on the TI 83 for the Population Mean!

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How to Find a Confidence Interval for the Mean on the TI 89

Instance trouble #1 (known standard deviation): L students at a Florida college have the following grade point averages: 94.viii, 84.1, 83.2, 74.0, 75.i, 76.2, 79.1, eighty.one, 92.1, 74.2, 64.2, 41.viii, 57.2, 59.ane, 65.0, 75.1, 79.2, 95.0, 99.8, 89.1, 59.2, 64.0, 75.one, 78.2, 95.0, 97.viii, 89.1, 65.ii, 41.9, 55.2. Find the 95% conviction interval for the population mean, given that σ = 2.27.

Step 1: Press APPS and scroll to Stats/List Editor. ENTER.

Step 2: Printing F1 and so 8. This clears the list editor.

Footstep three: Press Blastoff ) nine 2 to proper noun the list "CI2."

Step four: Enter your information in a listing. Follow each number with the ENTER key: 94.eight, 84.one, 83.2, 74.0, 75.1, 76.2, 79.1, 80.1, 92.1, 74.2, 64.ii, 41.8, 57.two, 59.1, 65.0, 75.one, 79.two, 95.0, 99.viii, 89.ane, 59.two, 64.0, 75.1, 78.2, 95.0, 97.8, 89.1, 65.2, 41.9, 55.2.

Footstep 5: Press F4 then 1.

Step 6: Enter "ci" in the "List" box: ALPHA key so ) 9 2.

Footstep 7: Enter 1 in the frequency box. Press ENTER. This should give y'all the mean (xbar, the get-go in the list) = 75.033.

Step 8: Press ENTER. Press 2nd F7 one ENTER. This brings up the z-distribution carte du jour.

Step ix: Press the right arrow key then the down arrow to select a "Data Input Method" of "Stats." Press ENTER.

Step x: Enter your σ from the question (in our case, 2.27), xbar from Step 7 (75.3033), n = 30 and the Confidence Interval from the question (in our example, information technology'south .95).

Step eleven: Printing ENTER and read the results. The "C Int" is {74.49,76.123}. This means we are 95% confident that the population hateful falls between 74.49 and 76.123.

That'due south it!

Example trouble #2 (unknown standard deviation): A random sample of 30 students at a Florida college has the following grade signal averages: 59.1, 65.0, 75.1, 79.two, 95.0, 99.8, 89.1, 65.ii, 41.ix, 55.two, 94.8, 84.i, 83.2, 74.0, 75.i, 76.two, 79.1, fourscore.1, 92.ane, 74.2, 59.ii, 64.0, 75.1, 78.2, 95.0, 97.8, 89.1, 64.2, 41.8, 57.2. What is the 90% conviction interval for the population mean?

Pace 1: Printing APPS. Coil to the Stats/Listing Editor and press ENTER.

Step ii: Printing F1 8 to clear the editor.

Step 3: Printing ALPHA ) 9 to name the list "CI."

Step iv: Enter your data in a list. Follow each number with the ENTER key: 59.1, 65.0, 75.1, 79.2, 95.0, 99.8, 89.1, 65.2, 41.9, 55.2, 94.eight, 84.1, 83.2, 74.0, 75.i, 76.ii, 79.1, 80.i, 92.1, 74.2, 59.ii, 64.0, 75.ane, 78.2, 95.0, 97.8, 89.1, 64.2, 41.8, 57.2.

Step five: Printing F4 1.

Step 6: Enter "ci" in the List box: Printing ALPHA ) 9.

Step 7: Enter1 in the frequency box. Press ENTER. This should give you the sample standard deviation, south_x = 15.6259, north = xxx, and x (the sample mean) = 75.033.

Step 8: Press ENTER. Press 2nd F2 2.

Footstep 9: Press the correct pointer key then the downwardly pointer to select a "Data Input Method" of "Stats." Printing ENTER.

Pace 10: Enter your x, s_x and n from Step 7. In our case, s_x = 15.6259. n = xxx and ten = 75.033.

Enter the Conviction Interval from the question (in our example, it's .ix).

Stride 11: Press ENTER and read the results. The C Int is {70.19,79.88} which ways that we are ninety% confident that the population mean falls between lxx.19 and 79.88.

That's it!

Tip: If yous know σ, utilize ZInterval instead of TInterval.
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How to discover a Confidence Interval for a Proportion on the TI 89

Example problem #ane: In a simple random sample of 295 students, 59.iv% of students agreed to a tuition increment to fund increased professor salaries. What is the 95% CI for the proportion in the entire student body who would agree?

Step 1: Printing APPS and coil downwards to Stats/List Editor. Printing ENTER.
If you don't come across the Stats/List editor, download it HERE from the TI-website. You'll need the graphlink cable that came with your estimator to transfer the software.

Step 2: Press second F2 5 for the i-PropZInt menu.

Stride 3: Effigy out your "successes." Out of 295 people, 59.four% said yes, so .694 × 295 = 175 people.

Step 4: Enter your answer from Step 3 into the Successes,x box: 175.

Stride five: Scroll down to n. Enter 295, the number in the sample.

Step 6: Scroll downwards to C Level. Enter the given confidence level. In our example, that's .95. Press ENTER twice.

Step 7: Read the result. The calculator returns the result C Int {.5372, .6493}. This ways that you lot are 95% confident that between 54% and 65% of the pupil torso agree with your decision.

Tip: If y'all are asked for a folder when entering the Stats Editor, simply press Enter. It doesn't affair which folder you employ.

Warning: Make sure your round your "success" entries to the nearest integer to avoid a domain error.

Example problem #ii: A contempo poll in a simple random sample of 986 women college students found that 699 agreed that textbooks were too expensive. Out of 921 men surveyed by the same fashion, 750 thought that textbooks were besides expensive. What is the 95% conviction interval for the difference in proportions between the two populations?

Step 1: Press APPS, curlicue to the Stats/List Editor, and printing ENTER.

Step 2: Printing 2nd F2 6 to reach 2-PropZint.

Step 3: Enter your values into the following boxes (Use "women" for population ane (x1 and n1) and "men" for population 2 (x2 and n2)):

• Successes, x1: 590*
• n1: 796
• Successes, x2: 548
• n2: 800
• C Level: 0.95

Step four: Printing ENTER.

Footstep five: Read the effect. The confidence interval is displayed at the peak equally C Int { .0119,.10053}. This means that your confidence interval is between 1.19% and 10.05%.

That's how to find a Confidence Interval on the TI 89!

Tip: As long as you keep rail of which population is x1/n1 and x2/n2, information technology doesn't matter which is entered in which box.

*Yous must enter a whole number hither, or yous'll get ERR:DOMAIN.

You'll come beyond this common type of problem in unproblematic stats: find a confidence interval given a large random sample and the number of "successes" in that sample.

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The 95% Confidence Interval Explained

The terms conviction level and confidence interval are ofttimes confused.

A 95% confidence level means is that if the survey or experiment were repeated, 95 percent of the time the data would match the results from the unabridged population. Sometimes you just can't survey anybody considering of time or cost (recall near how much it would cost to exercise a telephone survey of over 300 million Americans!).Therefore, you lot have a sample of the population. Having a 95% conviction level means that y'all're almost sure your results are the aforementioned as if y'all had surveyed everyone.

A 95% confidence interval gives you a very specific set of numbers for your confidence level. For example, let'due south suppose you were surveying a local school to see what the student'south state exam scores are. You set up a 95% conviction level and detect that the 95% confidence interval is (780,900). That ways if yous repeated this over and over, 95 percent of the time the scores would fall somewhere between 780 and 900.

Image: WUSTL.EDU

The to a higher place image shows a 95% conviction interval on a normal distribution graph. The scarlet "tails" are the remaining 5 percentage of the interval. Each tail has 2.5 percent (that's .025 as a decimal). Yous don't have to draw a graph when you're working with confidence intervals, but it can help y'all visualize exactly what you are doing — especially in hypothesis testing. If your results fall into the red region, and then that's exterior of the 95% confidence level that yous, as a researcher, set.

If you take a pocket-size sample or if you don't know the population standard deviation which in most real-life cases is true), so you'll find the 95% Confidence Interval with a t-distribution.

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Disproportionate Confidence Interval

An asymmetric confidence interval merely means that the bespeak estimate doesn't lie in the exact centre of the CI. You lot tin end upwards with asymmetric CIs for many reasons, including:

• You transform your data (for example, using log transformations).
• Y'all comprise random error.
• You incorporate systematic bias into the interval:
  • A positive systematic bias will increase the correct side of the interval.
  • A negative systematic bias will increase the left side of the interval.

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References

Kenney, J. F. and Keeping, East. S. "Confidence Limits for the Binomial Parameter" and "Confidence Interval Charts." §11.4 and 11.5 in Mathematics of Statistics, Pt. i, tertiary ed. Princeton, NJ: Van Nostrand, pp. 167-169, 1962.

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What Is The Value Of The T Score For A 99% Confidence Interval If We Take A Sample Of Size 10?,

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