Make a confidence interval for $p$ given the following values.
$x=314,n=500,C=99\%$

Since 1935, the Gallup Organization has conducted public opinion polls in the United States and around the world. The table shows the results of Gallup’s World Affairs Poll of 2021, in which 1021 U.S. adults were polled. The remaining percentages not shown in the results are adults who were not sure.

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Find the minimum sample size needed to estimate, with 95% confidence, the population proportion of adults who feel that China’s economic power is a critical or an important economic threat to the United States. Your estimate must be accurate within 2% of the population proportion.

Constructing Confidence Intervals In Exercises 27 and 28, use the figure, which shows the results of a survey in which 1021 U.S. adults were asked whether they see each of the possible threats to the vital interests of the United States as a critical threat in the next 10 years. (Source: Gallup)

Critical Threats Construct a 95% confidence interval for the population proportion of U.S. adults who gave each response.

In Exercises 9–12, construct the indicated confidence intervals for (a) the population variance and (b) the population standard deviation . Assume the sample is from a normally distributed population.

c = 0.98, s^2 = 278.1, n =41

In a survey of 2096 U.S. adults, 1740 think football teams of all levels should require players who suffer a head injury to take a set amount of time off from playing to recover. (Adapted from The Harris Poll)

d. Find the minimum sample size needed to estimate the population proportion at the 99% confidence level to ensure that the estimate is accurate within 3% of the population proportion.

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)"

"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)"