AP Stat Unit 7 Review

A scientist wants to test a hypothesis that a population mean is greater than 85. He gathers a sample of 40 measurements and the sample mean was 86.8 and the standard deviation was 8.2. What is the value of the test statistic for a one sample t test for population means?

• -0.22

• 0.22

• -1.39

• 1.39

A nutrition researcher is hoping to evaluate the claimed sugar content on the new McDonald's sandwich. McDonald's claims that their sandwich has 20g of sugar and a sample of 5 sandwiches shows the following sugar contents: 15, 22, 18, 17, and 23. What assumption(s) do we have to make in order to carry out a legitimate statistical test of the nutritionist’s claim?

I. The 5 sandwiches are from a normally distributed population.

II. The 5 sandwiches can be viewed as coming from a simple random sample.

III. The standard deviation of the population of all McDonald sandwich sugar content is known.

• I only

• II only

• III only

• I and II

• I, II and III

Michelin claims that their new snow tires for SUVs have a shorter skid distance than the current skid distance for their regular snow tires. The current mean skid distance for their snow tires is 140 feet. A tire testing company is hired to evaluate their claim. If μ represents the true mean skid distance for these new snow tires, which of the following states the null hypothesis and alternative hypothesis that should be tested?

• Ho: μ < 140; Ha: μ ≥ 140

• Ho: μ ≤ 140; Ha: μ > 140

• Ho: μ = 140; Ha: μ < 140

• Ho: μ = 140; Ha: μ ≤ 140

• Ho: μ = 140; Ha: μ ≠ 140

REMEMBER: 2-Tailed Probabilities are doubled

A large sample hypothesis test with σ known of a null hypothesis μ = 15 against the alternative hypothesis μ ≠ 15 results in the test statistic value of z = 1.37. Assuming σ is known, the corresponding p-value is approximately

• 0.0853

• 0.1707

• 0.4147

• 0.8293

• 0.9147

An assembly line machine is producing microchips for graphic cards that are 200 micrometers long. Each day, an SRS of five microchips are pulled and measured. If their mean length is under 195 micrometers or over 205 micrometers, the machinery is stopped and an engineer is called to make adjustments before production is resumed. The quality control procedure may be viewed as a hypothesis test with H0: μ = 200; Ha: μ ≠ 200. What would a Type II error result in?

• A necessary stoppage in microchip production.

• An unnecessary stoppage in microchip production.

• Continued production of wrong sized microchips.

• Continued production of proper sized microchips.

• Continued production of microchips that randomly are the right or wrong size.

An agronomist (an expert in the field of soil management and crop production) wanted to determine if a difference exists in the mean weight of watermelons grown in two separate fields (Field X and Field Y). A random sample of 42 watermelons was obtained from field X and the mean weight was 17 pounds and the standard deviation was 1.2 pounds. A random sample of 56 watermelons from field Y had a mean weight of 18.1 pounds and a standard deviation of 3.2 pounds. Calculate the value of the t test statistic for the mean difference in Field X – Field Y watermelon production.

• –3.112

• –2.361

• –2.091

• –1.355

• –0.878

Researchers wanted to determine what soccer ball would be able to be kicked further: one filled with helium or one filled with regular air. They recruited 15 people to participate in this study. Each person kicked the soccer ball filled with air and the soccer ball filled with helium, and the kicking distances, in yards, were recorded. The soccer ball that was kicked first was determined by the flip of a coin, and the participants did not know which soccer ball was filled with air and which was filled with helium. What type of study was conducted by the researchers and, of the following, which is the appropriate t-interval for inference?

• A completely randomized design and a t-interval for a difference between means for independent samples.

• A completely randomized design and a t-interval for a mean difference.

• A matched-pairs design and a t-interval for a difference between means for independent samples.

• A matched-pairs design and a t-interval for a mean difference.

• An observational study and a t-interval for a difference between means for independent samples.

A two-sided t-test for a population mean has a null hypothesis of H0: μ = 45. If a 90 percent t-interval constructed from the same sample data contains the value of 45, which of the following can be concluded about the test at a significance level of α = 0.10?

• The p-value is less than 0.10, and Ho should be rejected.

• The p-value is less than 0.10, and Ho should not be rejected.

• The p-value is greater than 0.10, and Ho should be rejected.

• The p-value is greater than 0.10, and Ho should not be rejected.

• There is not enough information given to make a conclusion about the p-value and Ho.

A consumer group is interested in the average times before a stove requires maintenance between two popular models on the market right now. An SRS of 12 of Model A's stoves is taken and an SRS of 15 of Model B's stoves is taken. The 95% confidence interval estimate of the mean difference is (3, 6). Which of the following is the most reasonable conclusion?

• The mean life expectancy of one model is twice that of the other.

• The mean life expectancy of one model is 3 years, while the mean life expectancy of the other is 6 years.

• The probability the life expectancies are different is 0.95.

• The probability the difference in life expectancies is greater than 6 years is 0.95.

• We are 95% confident that the difference in life expectancies is between 3 and 6 years.

Looking online, you find the salaries of all 25 players for the Chicago Cubs as of opening day of the 2021 baseball season. The club total was $128 million, 12th in the major leagues. Which inference procedure would you use to estimate the average salary of the Cubs players?

• One-sample z interval for μ

• One-sample t interval for μ

• One-sample t test

• One-sample z test

• None of these—this is not a situation that calls for inference.