"Finding p^ and q^ In Exercises 3–6, let p be the population proportion for the situation. Find point estimates of p and q.
Social Security In a survey of 351 retired Americans, 200 said that they rely on Social Security as major source of income. (Adapted from Gallup)"

Make a confidence interval for $p$ given the following values.

$x=314,n=500,C=99\%$

Make a confidence interval for $p$ given the following values.

$\hat{p}=0.15,n=60,C=90\%$

A health clinic is studying the effectiveness of a new flu vaccine. In a random sample of 80 patients who received the vaccine, 68 did not get the flu during the season. Make a 99% confidence interval for the true proportion of vaccinated individuals who are protected from the flu.

We are ___% confident that between (_––––,_––––) of vaccinated individuals are protected from the flu. 

"Finding p^ and q^ In Exercises 3–6, let p be the population proportion for the situation. Find point estimates of p and q.

Tax Fraud In a survey of 1040 U.S. adults, 62 have had someone impersonate them to try to claim tax refunds. (Adapted from Pew Research Center)"

Putting It Together: Lupus Based on historical birthing records, the proportion of males born worldwide is 0.51. In other words, the commonly held belief that boys are just as likely as girls is false. Systematic lupus erythematosus (SLE), or lupus for short, is a disease in which one’s immune system attacks healthy cells and tissue by mistake. It is well known that lupus tends to exist more in females than in males. Researchers wondered, however, if families with a child who had lupus had a lower ratio of males to females than the general population. If this were true, it would suggest that something happens during conception that causes males to be conceived at a lower rate when the SLE gene is present. To determine if this hypothesis is true, the researchers obtained records of families with a child who had SLE. A total of 23 males and 79 females were found to have SLE. The 23 males with SLE had a total of 23 male siblings and 22 female siblings. The 79 females with SLE had a total of 69 male siblings and 80 female siblings.

f. Does the sample evidence suggest that the proportion of male siblings in families where one of the children has SLE is less than 0.51, the accepted proportion of males born in the general population? Use the α = 0.05 level of significance.

In Problems 13–16, construct a confidence interval for p₁ - p₂ at the given level of confidence.

x₁ = 109, n₁ = 475, x₂ = 78, n₂ = 325, 99% confidence

In Problems 13–16, construct a confidence interval for p₁ - p₂ at the given level of confidence.

x₁ = 804, n₁ = 874, x₂ = 892, n₂ = 954, 95% confidence

The Process of Statistics: Metastatic Melanoma OPDIVA is a drug developed by Brystol-Meyers Squib that is meant to treat metastatic melanoma, which is the worst form of skin cancer. Survival rates for patients with this cancer are 6 to 10 months. Historically, patients with metastatic melanoma were treated with a combination of chemotherapy and dacarbazine. In clinical trials, 418 patients with metastatic melanoma were randomly assigned to either OPDIVO (n=210) by receiving 3 mg/kg by intravenous infusion every 2 weeks or dacarbazine (n=208) by receiving 1000 mg/m^2 by intravenous infusion every 3 weeks. Of the 210 patients in the OPDIVO group, 45 had survived 12 months; of the 208 patients in the dacarbazine group, 22 had survived 12 months.

d. Estimate the difference in proportion of patients who had survived 12 months in the OPDIVO group versus the dacarbazine group with 95% confidence. Interpret the interval.