4) A medical researcher is interested in knowing what percentage of the U.S. population has a certain gene. The researcher collect a random sample of 510 people from across the country, and tests them for the gene. The gene was present in 42 of the 510 people tested.

a) Find a 90% confidence interval for the true proportion of people in the U.S. with the gene.

b) Provide the right endpoint of the interval as your answer.

Round your answer to 4 decimal places.

1. Facebook penetration values (the percentage of a country’s population that are Facebook users) for 15 randomly selected countries are: 52.56, 33.09, 5.37, 19.41, 32.52, 41.69, 51.61, 30.12, 39.07, 30.62, 38.16, 49.35, 27.13, 53.45, 40.01.
   1. Give point estimates for the population mean Facebook penetration (µ), and the population standard deviation of Facebook penetration (_σ).
   2. Construct a 95% confidence interval estimation for µ. Interpret.
   3. Construct a 95% confidence interval estimation for _σ. Interpret.
   4. What assumptions do you need to make about the population so that the

confidence intervals given in (b) and (c) are valid?

1. While working for a polling company at C-Span, you are asked  to determine the percentage of the population that feel that the president has done a favorable job in handling the Pandemic.  You will take a SRS of adults in the USA.  We would like to be 95 % confident with a margin of error of 3 points.

1. If the last estimate done by FOX News was known to be 58%, what size of sample would be needed?   
2. Since you believe that the responses will be between 30% and 70% and you are not sure that previous estimate was accurate what estimate should you use? And what sample size would be needed?
3. If you would like to be 99% confident with a margin of error of 3 points and unsure of the last estimate, what sample size would be needed?
4. Comment about the difference between answers of b and c.  Also why would a polling company use 95% rather than 99%?

Write a report to your boss at C-Span, explaining to her what you are doing.

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .35.

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)? Use 95% confidence.

b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?

1.We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of +/-0.08 at 95% confidence?

A.301

B.150

C.300

D.151

2.We have created a 95% confidence interval for the population mean with the result [10, 15]. What decision will we make if we test H0: m = 16 versus H1: m ¹ 16 at 10% level of significance?

A.Fail to reject H0 in favor of H1

B.Reject H0 in favor of H1

C.We cannot tell what our decision will be from the information given

D.Accept H0 in favor of H1

3.Suppose we want to test H0: m ³ 28 versus H1: m < 28. Which one of the following possible sample results based on a sample of size 36 is most likely to reject H0 in favor of H1?

A.Sample mean = 26, sample standard deviation = 9

B.Sample mean = 24, sample standard deviation = 4

C.Sample mean = 28, sample standard deviation = 2

D.Sample mean = 25, sample standard deviation = 6

4.If a null hypothesis is rejected at the 5% level of significance, it

A.will never be tested at the 1% level

B.will always be rejected at the 1% level

C.may be rejected or not rejected at the 1% level

D.will always be accepted at the 1% level

it is reported that the percentage of males 18 and older who have never been married is greater than the percentage of females 18 and over who have never been married. in a particular county, out of 50 males surveyed, 32% had never been married. while out of 40 females, 25% had never been married. conduct a hypothesis to determine if the proportion of men is greater than the proportion of women. let confidence level=0.05. use the p-value method.

A nutritionist is interested in determining the percentage of American adults who eat salad at least once a week. She takes a random sample of 200 American adults and finds that 176 of them eat salad at least once a week. Find a 95% confidence interval for the true proportion of American adults who eat salad at least once a week. Due to the different methods, round OUT and give 2 decimal places. Select the best possible answer.

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .28.

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)? Use 95% confidence.

b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?

I would like to test a hypothesis that the percentage of people who consider themselves as conservatives today is lower than it was 20 years ago. Conveniently enough, my old professor has data from 20 years ago when he conducted a similar survey. The number of people 20 years ago who identified as conservative in his survey was 314 out of 612 total. I conduct a survey today and find that out of the 415 people i surveyed, 198 considered themselves to be conservative. If i wish to present my findings with a level of significance of .05, what conclusion would i draw?

options:

based on the data, there's evidence of a decrease in those who identify as conservative.

based on the data, there's no evidence of a decrease in those who identify as conservative.

based on the data, there's evidence of an increase in those who identify as conservative.

based on the data, there's no evidence of an increase in those who identify as conservative.