3.2.10A recent study examined hearing loss data for 1,771 U.S. teenagers. In this sample, 333 were found to have some level of hearing loss. News of this study spread quickly, with many news articles blaming the prevalence of hearing loss on the higher use of ear buds by teens. At MSNBC.com (8/17/2010), Carla Johnson summarized the study with the headline: "1 in 5 U.S. teens has hearing loss, study says." To investigate whether this is an appropriate or a misleading headline, you will conduct a test of significance with the following hypotheses:

Null:=0.20

Alternative:0.20

Question A: Read question 3.2.10 but answer these questions (not the ones provided in the book)

a) Describe what the symbol pi stands for in this context.

b) State n and the value of the sample proportion p_hat

c) Use R (the rflip command) to carry out a simulation to find the approximate p-value.Use set.seed(123) and 10,000 repetitions.

d) Now use R to carry out a simulation to find the sampling distribution to estimate the value of pi.Use rflip(n, p_hat) where p_hat is the value you got in (b).What is the standard deviation of the sampling distribution? Again, use set.seed(123) and 10,000 repetitions.

e) Find the 2*SD confidence interval for estimating pi.

f) What is the margin of error for this confidence interval?

g) What is the confidence level for this confidence interval?

h) Based on the confidence interval, is 0.20 a plausible value for pi?i) Using a significance level of 0.05, based on your p-value, is 0.20 a plausible value for pi?

Question B:

Suppose that we attempt to estimate the proportion of the U.AS. population that is left-handed.

a) Survey A is based on a random sample of 20 people and finds that .10 are left-handed. Simulate the sampling distribution to estimate the proportino of all left-handed people in the population.Use set.seed(234) and 10,000 repetitions.Provide a histogram of the sampling distribution and describe the shape.

b) What is the standard deviation of the sampling distribution in (a)?

c) Survey B is based on a random sampel of 200 people and also finds that .10 are left-handed.Simulate the sampling distribution using set.seed(234) and 10,000 repetitions. Provide a histogram of the sampling distribution and describe the shape.

d) What is the standard devation of the samplign distribution in (c).

e) For which of these surveys would a 2*SD approach to finding a 95% confidence interval be appropriate? Choose one resopnse and explain your choice:

i) Both surveys

ii) Only survey A

iii) Only survey B

iv) Neither survey A or B

f) If you selected (i)-(iii), provide the 2*SD confidence interval for the proportion of left-handed people among the entire population.