Confidence Intervals

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AP Statistics › Confidence Intervals

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1

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2

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3

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4

An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500.

Provide a 98% confidence interval for the true mean cost of repair.

Explanation

Standard deviation for the samle mean:

Since n < 30, we must use the t-table (not the z-table).

The 98% t-value for n=24 is 2.5.

5

An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500.

Provide a 98% confidence interval for the true mean cost of repair.

Explanation

Standard deviation for the samle mean:

Since n < 30, we must use the t-table (not the z-table).

The 98% t-value for n=24 is 2.5.

6

An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500.

Provide a 98% confidence interval for the true mean cost of repair.

Explanation

Standard deviation for the samle mean:

Since n < 30, we must use the t-table (not the z-table).

The 98% t-value for n=24 is 2.5.

7

The population standard deviation is 7. Our sample size is 36.

What is the 95% margin of error for:

  1. the population mean

  2. the sample mean

  1. 13.720

  2. 2.287

  1. 11

  2. 3

  1. 12.266

  2. 3.711

  1. 14.567

  2. 4.445

  1. 15.554

  2. 3.656

Explanation

For 95% confidence, Z = 1.96.

  1. The population M.O.E. =

  1. The sample standard deviation =

The sample M.O.E. =

8

The population standard deviation is 7. Our sample size is 36.

What is the 95% margin of error for:

  1. the population mean

  2. the sample mean

  1. 13.720

  2. 2.287

  1. 11

  2. 3

  1. 12.266

  2. 3.711

  1. 14.567

  2. 4.445

  1. 15.554

  2. 3.656

Explanation

For 95% confidence, Z = 1.96.

  1. The population M.O.E. =

  1. The sample standard deviation =

The sample M.O.E. =

9

The population standard deviation is 7. Our sample size is 36.

What is the 95% margin of error for:

  1. the population mean

  2. the sample mean

  1. 13.720

  2. 2.287

  1. 11

  2. 3

  1. 12.266

  2. 3.711

  1. 14.567

  2. 4.445

  1. 15.554

  2. 3.656

Explanation

For 95% confidence, Z = 1.96.

  1. The population M.O.E. =

  1. The sample standard deviation =

The sample M.O.E. =

10

The confidence interval created for the difference in means between two training programs for middle distance college runners is . The variable being measured is the improvement in seconds of mile times over the course of a season. One program has more speed work and intervals, while the other focuses more on distance training.

What does the confidence interval tell us about the difference in the two programs?

Zero is in the interval, so do not reject the null. There is no evidence that one program is better than the other.

is greater than , so reject the null. This is evidence that one program is better at reducing mile times than the other.

Zero is not in the interval, so reject the null. This is evidence that one program is significantly better at reducing mile times.

The confidence interval is large, so one program is clearly better at reducing mile times than the other.

The mean improvement of second is too small to matter, so reject the null. There is no evidence that one program is better at reducing miles times.

Explanation

For there to be a statistically significant difference in the training programs, the 95% confidence interval cannot include zero. includes zero, so we can't say that one program is significantly better than the other.

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