Watches and bacteria:A group of researchers investigated the contamination of medical personnel watches at a New York hospital, since there is a potential for patient exposure to potentially dangerous bacteria.

They sampled watches worn by physicians, physician assistants, and medical students at a teaching hospital in New York. Nearly half (47.2%) of the watches tested harbored microorganisms that can cause illness. By comparison, only one of the 10 watches worn by security guards tested positive for a disease-carrying microorganism. The researchers want to determine if the difference is statistically significant.

Which of the following is an appropriate statement of the null hypothesis, H0?

1. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0:p
2. = 47.2%.
3. The proportion of contaminated wrist-watches from medical personnel is not the same as the proportion of contaminated wrist-watches from security guards, i.e., H0:p
4. not equal 47.2%.
5. The proportion of contaminated wrist-watches from medical personnel is greater than the proportion of contaminated wrist-watches from security guards, i.e., H0:p
6. > 47.2%.

In 2010 polls indicated that 76% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 69% favor mandatory testing for this purpose. Has public opinion changed since 2010?

We test the hypothesis that the percentage supporting mandatory testing is less than 76% this year. Thep

-value is 0.014.

Which of the following interpretation of thisp

-value is valid?

1. If 76% of Americans still favor mandatory testing this year, then there is a 1.4% chance that poll results will show 69% or fewer with this opinion.
2. There is a 1.4% chance that the null hypothesis is true.
3. The probability that Americans have changed their opinion on this issue since 2010 is 0.014.

A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 3.6% of them are worn out. With this data, we test the following hypotheses.

H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.

Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.

What assumption about the sample underlies the hypothesis test?

1. The sample comes from a population of tires where 250 are used for 60,000 miles.
2. The sample comes from a population of 250 tires that have a 60,000 mile warranty.
3. The sample comes from a population of tires with 60,000 miles where 5% of tires are worn out.
4. The sample comes from a population of tires with 60,000 miles where 3.6% of the tires are worn out.

Pregnancy testing:A college student hasn't been feeling well and visits her campus health center. Based on her symptoms, the doctor suspects that she is pregnant and orders a pregnancy test. The results of this test could be considered a hypothesis test with the following hypotheses:

• H0: The student is not pregnant
• Ha: The student is pregnant.

Based on the hypotheses above, which of the following statements is considered aType II error?

1. The student is not pregnant, but the test result shows she is pregnant.
2. The student is pregnant, but the test result shows she is not pregnant.
3. The student is not pregnant, and the test result shows she is not pregnant.
4. The student is pregnant, and the test result shows she is pregnant.

Living with parents:The Pew Research Center reported that 36% of American Millennials (adults ages 18-31) still live at home with their parents. A group of students wants to conduct a study to determine whether this result is true for students at their campus. They survey 300 randomly selected students at their campus and determine that 43% of them still live at home with their parents. With this data, they test the following hypotheses at the 5% significance level. The p-value is 0.006.

H0: Of Millennial students at their campus, 36% live at home with their parents.

Ha: More than 36% of Millennial students at their campus live at home with their parents.

What can we conclude?

1. Nothing. The sample size is too small to represent students at their campus.
2. The evidence suggests that more than 36% of students at their campus live at home with their parents because 43% is greater than 36%.
3. The evidence suggests that more than 36% of students at their campus live at home with their parents because the p-value is less than the significance level.
4. The evidence does not suggest that more than 36% of students at their campus live at home with their parents because the difference between 43% and 36% is not statistically significant. A 7% difference could be due to random chance.

In 2016, theCenters for Disease Control(CDC) reported that the teen birth rate in Georgia was 24.4%. The Atlanta City Council orders a study to see if the teen birth rate within the city of Atlanta is lower.

https://www.cdc.gov/nchs/pressroom/sosmap/teen-births/teenbirths.htm

Suppose that a study of1000

female teenagers in Atlanta found that 234 of them gave birth in 2016.

Given that the population proportion is understood to bep

= 0.244, what would be the null hypothesis, H0, for this study?

1. Ha:p= 24.4%
2. H0:p< 24.4%
3. H0:p= 23.4%
4. H0:p= 24.4%