AP Statistics Hypothesis Tests for Means

A report on a certain fast food restaurant states that , the mean order total, is $9. The manager of the restaurant believes the mean is higher. A random sample of orders will be selected. The sample mean will be calculated and used in a hypothesis test to investigate the belief. Which of the following is the correct set of hypotheses?

A company that manufactures laptop batteries claims the mean battery life is 16 hours. Assuming the distribution of battery life is approximately normal, a consumer group will conduct a hypothesis test to investigate whether the battery life is less than 16 hours. The group selected a random sample of 14 of the batteries and found an average life of 15.6 hours with a standard deviation of 0.8 hour. Which of the following is the correct test statistic for the hypothesis test?

Researchers are testing a new diagnostic tool designed to identify a certain condition. The null hypothesis of the significance test is that the diagnostic tool is NOT effective in detecting the condition. For the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective. Which of the following should the researchers do to avoid the more consequential error?

• Increase the significance level to increase the probability of Type I error

• Increase the significance level to decrease the probability of Type I error.

• Decrease the significance level to increase the probability of Type I error

• Decrease the significance level to decrease the probability of Type I error.

A marketing executive is investigating whether this year’s advertising campaign has resulted in greater mean sales compared with last year’s mean sales. The executive collects a random sample of 100 customer orders from a large population of orders and calculates the sample mean and sample standard deviation. Which of the following is the appropriate test for the executive’s investigation?

• A one-sample -test for a population mean

• A one-sample -test for a population mean

• A one-sample -test for a population proportion

• A two-sample -test for a difference between means

• A matched-pairs -test for a mean difference

Milk has a PH of 6.7, which is slightly acidic. Cheese makers add a culture to milk to lower the PH, making it more acidic and turning it into cheese. A manufacturer is experimenting with a new culture that claims to produce a PH of 5.2, which is perfect for cheddar cheese. A set of 50 test batches resulted in an average PH of 5.11. A one sample -test was conducted to investigate whether there is evidence that the mean PH is different from 5.2. The test resulted in a PH-value of 0.018. Which of the following is a correct interpretation of the -value?

• The probability that the true PH is equal to 5.2 is 0.018.

• The probability that the true PH is different from 5.2 is 0.018.

• The probability of observing a sample mean of 5.11 or less is 0.018 if the true mean is 5.2.

• The probability of observing a sample mean of 5.11 or more is 0.018 if the true mean is 5.2.

• The probability of observing a sample mean of 5.11 or less, or of 5.29 or more, is 0.018 if the true mean is 5.2.

A company director investigated whether there is a difference in the mean number of overtime hours worked each

week by employees assigned to two different managers. Each manager, A and B, manages 100 employees. Random

samples of 35 employees from manager A and 40 employees from manager B were selected. The number of

overtime hours worked was recorded for the 75 employees each week. Have the conditions been met for inference with a confidence interval for the difference in the population means?

• Yes, all conditions have been met.

• No, because the data were not collected using a random method.

• No, because the size of at least one of the samples is greater than 10 percent of the population.

• No, because the sample sizes are not large enough to assume the distribution of the difference in sample

  means is normal.

• No, because the sample sizes are not the same.

At the Chrysler manufacturing plant, there is a part that is supposed to weigh precisely 19 pounds. The engineers take a sample of parts and want to know if they meet the weight specifications. What are our null and alternative hypotheses?

• H_o : μ = 17, H_a : μ ≠ 19

• H_o : μ = 19, H_a : μ ≠ 19

• H_o : μ = 19, H_a : μ ≠ 17

• H_o : μ = 17, H_a : μ ≠ 17

Dannon is supposed to put 29.6 grams of fruit in their fruit-flavored yogurt. To see if enough fruit is being placed in cups of fruit-flavored yogurt, a quality inspector measured the amount in 27 containers.She found an average of 28.9 grams of fruit and standard deviation of 2.8 grams. Does this show that there is probably enough yogurt in the cups?

• One-Sample T Test for a Mean

• One-Sample Z Test for a Proportion

• Matched-Pairs T Test for a Mean

• Chi-Square Goodness of Fit Test

A manufacturer claims that his tires last at least 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.

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

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

When p-value is greater than alpha we:

• Accept Ho

• Accept Ha

• Fail to reject Ho

• Reject Ho