AP Stats review Testing for means, chi-squared, slope

A P-value indicates:

• the probability that the null hypothesis is true

• the probability that the alternative hypothesis is true

• the probability of obtaining the results (or one more extreme) if the null hypothesis is true

• probability of a Type I error

Answer explanation

A P-value indicates the probability of obtaining the results (or one more extreme) if the null hypothesis is true.

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

• a) Reject the null hypothesis

• b) Reject the alternative hypothesis

• c) Fail to reject the null hypothesis

• d) Fail to reject the alternative hypothesis

Answer explanation

The appropriate conclusion is to reject the null hypothesis since the P-value is less than the significance level (0.0304 < 0.05).

A manufacturer claims that his tires average 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles. You do not think that the tires average 40,000 miles.

Test the Manufacturer’s claim at α = .01.

Step 1: Write the null and alternative hypothesis.

• H₀ = 40,000

  H_a = 40,000

• H₀ = 40,000

  H_a > 40,000

• H₀ = 40,000

  H_a < 40,000

• H₀ = 40,000

  H_a ≠ 40,000

Answer explanation

The correct choice is H0 = 40,000 and Ha ≠ 40,000 because we are testing if the tires average is not equal to the claimed value.

A manufacturer claims that his tires average 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles. You do not think that the tires average 40,000 miles.

Test the Manufacturer’s claim at α = .01.

Step 2a: Determine if it is a z-test or a t-test.

• z-test because the population standard deviation is known.

• z-test because the population standard deviation is unknown.

• t-test because the population standard deviation is known.

• t-test because the population standard deviation is unknown.

Answer explanation

This is the explanation for the answer.

A manufacturer claims that his tires average 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles. You do not think that the tires average 40,000 miles.

Test the Manufacturer’s claim at α = .01.

Step 2b: Calculate the z-score or t-score.

• z = -3.23

• z = -0.65

• t = -3.23

• t = -0.65

Answer explanation

The correct choice is t = -3.23 because we are testing the mean of a sample against a known population mean, so we use a t-score for hypothesis testing.

A manufacturer claims that his tires average 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles. You do not think that the tires average 40,000 miles.

Test the Manufacturer’s claim at α = .01.

Step 4: Determine your conclusion.

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

Answer explanation

Provide your answer explanation here.

A manufacturer claims that his tires average 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles. You do not think that the tires average 40,000 miles.

Test the Manufacturer’s claim at α = .01.

Step 5: Interpret your conclusion.

• There is enough evidence to suggest that the tires do not average 40,000 miles.

• There is not enough evidence to suggest that the tires do not average 40,000 miles.

Answer explanation

There is enough evidence to suggest that the tires do not average 40,000 miles.

Tags

CCSS.HSS.IC.B.4

The mean height of women in America is 64 inches. The manager at a clothing store has noticed that a lot of women in her city are having to get their dresses hemmed because they are too long. She thinks that the women in her city are actually shorter than 64 inches. She takes a random sample of 16 women and finds their height to be 61.75 inches with a standard deviation of 2.7 inches. Test the claim that the average woman is 64 inches tall at an alpha-level of 0.05.

Step 3: Find the p-value to represent the scenario.

• p = 0.0004

• p = 0.2033

• between 0.001 and 0.0025

• between 0.002 and 0.005

Answer explanation

The p-value falls between 0.001 and 0.0025, indicating that we reject the null hypothesis and conclude that the average height of women in the city is significantly different from 64 inches.

The mean height of women in America is 64 inches. The manager at a clothing store has noticed that a lot of women in her city are having to get their dresses hemmed because they are too long. She thinks that the women in her city are actually shorter than 64 inches. She takes a random sample of 16 women and finds their height to be 61.75 inches with a standard deviation of 2.7 inches. Test the claim that the average woman is 64 inches tall at an alpha-level of 0.05.

Step 4: Determine your conclusion.

• Reject the Ho

• Fail to reject the Ho

• Reject the Ha

• Fail to reject the ha

Answer explanation

Provide your answer explanation here.

How many degrees of freedom will be present?

• 4

• 5

• 6

• 7

Answer explanation

The correct answer is 6 because in statistics, degrees of freedom refer to the number of values in the final calculation of a statistic that are free to vary.