1

Select one answer.

10 points

Does secondhand smoke increase the risk of a low birthweight? A baby is considered have low birthweight if he/she weighs less than 5.5 pounds at birth. According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birthweight.

Suspecting that the national percentage is higher than 7.8%, researchers randomly select 1,200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy and find that 10.4% of the sampled babies are categorized as low birth weight.

Let p be the proportion of all babies in the United States who are categorized as low birth weight. What are the appropriate null and alternative hypotheses for this research question?

1. H₀: p = 0.078

   H_a: p 0.078

2. H₀: p = 0.078

   H_a: p > 0.078

3. H₀: p = 0.104

   H_a: p 0.104

4. H₀: = 0.078

   H_a: > 0.078

Question 2

Select one answer.

10 points

A manufacturer of t-shirts marks a shirt as irregular when it has defects such as crooked seams, stains, rips, or holes. A small number of irregular t-shirts are expected as part of the manufacturing process, but if more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process.

In order to test whether his plant is making a higher than expected number of irregular t-shirts, the manager of a plant randomly selects 100 t-shirts and finds that 12 are irregular.

He plans to test the hypotheses: H₀, P = 0.08, versus H_a, p > 0.08 (where p is the true proportion of irregular t-shirts). What is the test statistic?

1. Z = 1.47
2. Z = 5
3. Z = 1.47
4. Z = 1.23

Question 3

Select one answer.

10 points

A researcher wants to find out if U.S. adults still support the death penalty at a proportion of 0.64 (as it was in 2003). This graph indicates the sampling distribution for the proportion of supporters in random samples of 25 adults. The standard deviation is approximately 0.10.

What is the approximate test statistic for p = 0.84?

1. 2
2. 1
3. 0
4. 1
5. 2

Question 4

Select one answer.

10 points

The proportion of college football players who have had at least one concussion is estimated to be 34% in the United States. We wanted to know if football players at our university were less likely to have suffered a concussion, so we surveyed a random sample of 100 past and present football players at our university. Is this survey valid or not valid for testing the hypothesis that the proportion of college football players at our university with at least one concussion is less than the national average?

1. Valid
2. Not valid

Question 5

Select one answer.

10 points

According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She obtained a list of 25 randomly selected students from the population of all students at her university by requesting this information from the universitys institutional research office. She collected the responses and calculated that the proportion for her university was 43%.

Which one of the following statements about the z-test is correct?

1. It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one).
2. It is not safe to use the z-test for p, since n * p_ois not large enough.
3. It is not safe to use the z-test for p, since n * (1 p_o) is not large enough.
4. It is safe to use the z-test for p.

Question 6

Select all that apply.

10 points

A national poll by the Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. Dr. Blackman wanted to find out if her public nonprofit university had a lower proportion of students who graduated with student loan debt in 2013.

For this survey, the null hypothesis was that the proportion of students with graduated with student loan debt equals 69% and the alternative hypothesis is that the proportion with student loan debt does not equal 69%. The significance level for this test was 0.05.

The results of the hypothesis test of the new survey showed a p-value of 0.039.

Which of the following statements is correct? Check all that apply.

1. The results were statistically significant.
2. The results were not statistically significant.
3. The null hypothesis should be rejected.
4. The null hypothesis should be accepted.
5. The null hypothesis cannot be rejected.