A city planner is comparing traffic patterns at two different intersections. He randomly selects 12 times between 6 am and 10 pm, and he and his assistant count the number of cars passing through each intersection during the 10 minute interval that begins at that time. He plans to test the hypothesis that the mean difference in the number of cars passing through the two intersections during each of those 12 times intervals is 0. Which of the following is the appropriate test of the city planner’s hypothesis?

• Two-proportion z-test

• Two-sample z-test

• Matched pairs t-test

• Two proportion t-test

• Two-sample t-test

We wish to test if the two varieties are significantly different in their mean carbohydrate content. Which of the following are the appropriate null and alternative hypotheses for this situation?

Assuming the conditions for inference were met, which of the following is the most appropriate conclusion to draw at the α = 0.05 level?

• The test provides convincing evidence that the carbohydrate content of variety 1 is higher

  than variety 2.

• The test provides convincing evidence that the carbohydrate contents of the two varieties

  are equal.

• We accept Ha: variety 1 has a higher carbohydrate content than variety 2.

• We reject Ho: variety 1 has a higher carbohydrate content than variety 2.

• We cannot reject Ho: we do not have convincing evidence that the carbohydrate contents

  are different.

Popular wisdom is that eating presweetened cereal tends to increase the number of dental caries (cavities) in children. A sample of children was (with parental consent) entered into astudy and followed for several years. Each child was classified as a sweetened-cereal lover or an unsweetened cereal lover. At the end of the study, the amount of tooth damage was measured. Here are the summary data:

Cereal preference n Mean Std. Dev.

Sweetened 10 6.41 5.0

Unsweetened 15 5.20 15.0

Assuming the necessary conditions for inference are met, which of the following is an approximate 95% confidence interval for the difference in the mean tooth damage?

Tags

CCSS.HSS.IC.B.4

You are constructing a 90% confidence interval for the difference of means from simplen random samples from two independent populations. The sample sizes are n1 = 6 and n2 =14. You draw dot plots of the samples to check the normality condition for two-sample tprocedures. Which of the following descriptions of those dot plots would suggest that it is safe to use t-procedures?

I. The dot plot of sample 1 is roughly symmetric, while the dot plot of sample 2 is moderately skewed left. There are no outliers.

II. Both dot plots are roughly symmetric. Sample 2 has an outlier.

III. Both dot plots are strongly skewed to the right. There are no outliers.

• I only

• II only

• III only

• I, II, and III

• t-procedures are not recommended in any of these cases.

Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Asheville, and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Lincoln. They intend to perform a test of significance on their data, using the hypotheses

Ho : pA − pL = 0 versus Ha : pA − pL ≠ 0 and the 0.05 significance level.

When calculating the test statistic, what expression would they use to estimate the standard deviation of the sampling distribution of the difference in proportions?

Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Asheville, and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Lincoln. They intend to perform a test of significance on their data, using the hypotheses

Ho : pA − pL = 0 versus Ha : pA − pL ≠ 0 and the 0.05 significance level.

Janice and Linda’s test statistic is 1.07. Which of the following is closest to the appropriate P-value for the test?

• 0.0446

• 0.0892

• 0.1423

• 0.1449

• 0.2846

Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Asheville, and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Lincoln. They intend to perform a test of significance on their data, using the hypotheses

Ho : pA − pL = 0 versus Ha : pA − pL ≠ 0 and the 0.05 significance level.

Which of the following best describes what it would mean if Janice and Linda’s test resulted in a Type I error?

• Concluding that there is a difference in the proportion of rainy days in the two cities when

  there is no difference.

• Concluding that there is no difference in the proportion of rainy days in the two cities when

  there is a difference.

• Choosing the wrong test procedure, such as using a z-test instead of a t-test.

• Accepting the alternative hypothesis instead of rejecting the null hypothesis.

• Accepting the null hypothesis instead of rejecting the alternative hypothesis.