AP Statistics Chapter 11

Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are Normally distributed with mean μ . A representative of a consumer advocacy group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses Ho :μ =14 Ha :μ <14 A Type I error in this situation would mean

• concluding that the bags are being underfilled when they actually aren’t

• concluding that the bags are being underfilled when they actually are.

• concluding that the bags are not being underfilled when they actually are.

• concluding that the bags are not being underfilled when they actually aren’t.

• none of these

A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses H0 : µ = 12 versus Ha: µ < 12 was conducted, where µ represents the population mean number of ounces of the beverage dispensed per bottle by the machine. The p-value for the test was 0.08. Which of the following is the most appropriate conclusion to draw at the significance level of α = 0.05?

• Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

• Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.

• Because the p-value is greater than the significance level, there is not convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.

• Because the p-value is less than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

• Eight percent of the bottles will be filled with less than 12 ounces.

A market researcher suspects that employees at Company A were older on average than employees at company B. They obtained a random sample of employees ages from each company. Results are shown. What should the researcher conclude at the 5% significance level?

• There is strong evidence that employees at company A are older than those at company B.

• There is strong evidence that employees at company B are older than those at company A.

• There is no difference in the ages of employees at companies A & B.

• The independent assumption is violated; no conclusions can be made.

A market researcher suspects that employees at Company A were older on average than employees at company B. They obtained a random sample of employees ages from each company. Results are shown. What is the p-value?

• 3.07

• 0.00163

• 57.7

• 0.0032

A market researcher suspects that employees at Company A were older on average than employees at company B. They obtained a random sample of employees ages from each company. Results are shown. Which is the correct calculation for the t-statistic?

• 
• 
• 
• 

This test is used to compare the responses to a treatment in a within-groups design (ie, does an SAT prep course improve an individual’s SAT scores?). A listening test was administered to Spanish teachers before and after an institute designed to improve Spanish listening skills. The maximum possible score on the test was 36. The Pre- and Post-test results for each subject are listed below: Sub 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Pre 30 28 31 26 20 30 34 15 28 20 30 29 31 29 34 20 26 25 31 Pos 29 30 32 30 16 25 31 18 33 25 32 28 34 32 32 27 28 29 32 Determine if the institute improved listening skills at the 5% significance level.

• 1-sample t-test

• 1-sample t-test (mean difference)

• 2-sample t-test (difference in means)

A study of road rage asked separate random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0 to 20. Are the conditions for performing a two-sample t test satisfied?

• Yes; we have two independent random samples and large samples.

• Maybe; we have independent random samples, but we need to look at the data to check for Normality.

• No; road rage scores in a range between 0 and 20 can't be Normal.

• No; we don't know the population standard deviation.

• Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.

A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys. She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10. She does the same thing for the boys.

• 1-sample t-test. The teacher should compare the sample mean for the girls against the population mean for the boys.

• Paired t-test. Since the boys and girls are in the same class, and are hence dependent samples, they can be linked.

• Either two-sample or paired t-test will work.

• Two-sample t-test. There is no natural pairing between the two populations.

• Paired t-test. Since there are 10 boys and 10 girls, we can link the two samples.

A researcher is interested in investigating whether people perform better at dexterity tests while listening to classical music or to no music. He designs a dexterity test, and first gives it to his participants while classical music is playing, and then while no music is playing.

• z-test, since the researcher can find the standard deviation of his population.

• Not enough information is given to determine the best type of test.

• Paired t-test, since there are two sets of measurements on the same subjects, providing a natural linking.

• Two-sample t-test, since how a subject performs with music should have no influence on how he performs without music, creating two independent samples.

• 1-sample t-test, since there is only one sample of subjects taking the dexterity tests.

An agricultural company wanted to know if a new insecticide would increase corn yields. Eight test plots showed an average increase of 3.125 bushels per acre. The standard deviation of the increases was 2.911 bushels per acre. Determine a 99% confidence interval for the mean increase in yield.

• (-0.476, 6.726)

• (-6.726, -4.399)

• (-0.476, 4.399)

• (1.851, 6.726)

• (1.851, 4.399)