1. Researchers are interested in determining whether more women than men prefer the beach to the mountains. In a random sample of 200 women, 45% prefer the beach, whereas in a random sample of 300 men

1. Researchers are interested in determining whether more women than men prefer the beach to the mountains. In a random sample of 200 women, 45% prefer the beach, whereas in a random sample of 300 men, 52% prefer the beach. What is the 99% confidence interval estimate for the difference between the percentages of women and men who prefer the beach over the mountains?

a.  − 0.07 ± 0.1172

b. − 0.07 ± 0.0557

c. − 0.07 ± 0.0053

d. 0.07 ± 0.01172

e. 0.07 ± 0.0053

2. A researcher wants to test the claim that the proportion of men and women who exercise regularly is not the same. He finds that 42 of 65 randomly selected men and 34 of 52 randomly selected women report exercising regularly. A 90% confidence interval for the difference in population proportions is (−0.154, 0.138). Which of the statements gives the correct outcome of the researcher's test of the claim?

a.     Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly is the same. 

b.    Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly may be the same. 

c.     Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly is different. 

d.    Because the confidence interval includes more positive than negative values, the researcher can conclude that a greater proportion of men than women exercise regularly. 

e.     The researcher cannot draw a conclusion about a claim without performing a significance test.

3. A children's cancer research fund has been set up to collect donations for the treatment and research of the disease. A random sample of 600 people shows that 47% of the 300 who were contacted by telephone actually made contributions, compared with only 34% of the 300 who received email requests. Which of the formulas calculates the 98% confidence interval for the difference in the proportions of people who make donations when contacted by telephone versus those contacted by email?

I attached screenshots of these answer choices.

4. A researcher wants to determine whether there is a relationship between age and frequency of travel. In a random sample of 18- to 25-year-olds, 70 of 195 traveled more than twice each year. In a random sample of 55- to 62-year-olds, 205 of 230 traveled more than twice each year. What is the margin of error for a 98% confidence interval for the difference between the proportions of travelers in these age groups who travel more than twice each year?

a.     1.3180

b.    0.5656 

c.     0.0931 

d.    0.0400 

e.     0.0016

5. A simple random sample (SRS) of 150 is taken from a population with a 0.6 proportion of success. An independent SRS of 250 is taken from a population with a 0.3 proportion of success. What is the standard deviation of the sampling distribution for the difference in sample proportions?

a.     0.0011 

b.    0.0024

c.     0.0212

d.    0.0494

e.     None of the above