A state’s Department of Commerce reports that 82 percent of all small businesses that applied for a loan were approved. That claim makes us wonder if it is accurate If we wanted the true proportion of all applicants that were approved with 95 percent confidence and be within 5.25 percent of the true proportion, how many applications should they sample?   Suppose that we took a random sample of 1200 and found that 994 were approved for their applied loan. Is there reason to be alarmed about the claim? Build a 98 percent confidence interval. Interpret what 98 percent confidence means in this context

1. The percentage of 12- to 17-year-olds who reported talking at least once in the past year with their parents about the dangers of drug, tobacco, or alcohol is 60% nationally. A state youth council believes this proportion is higher in their state, where there has been an intense media campaign about this issue. A survey of randomly chosen students from across the state shows 1032 of 1642 students reporting they are having these conversations with their parents. Is there evidence that the percent of students using drugs, tobacco or alcohol in this state is above the national rate?

9. A researcher wants to construct a 99% confidence interval for the proportion of Americans who think that the U.S. invading Iraq was an effective step in combating world terrorism. She has no initial idea of what that proportion is. How large should her sample size be if she wants the margin of error to be at most two percent? Show or explain your thinking.

There is a 75% chance that those who are called will serve on jury duty.  If 12 people are called for jury duty, what is the probabilty that none of the people will serve on the jury?

A research company is interested in determining the true proportion of Americans that work remotely. In a random sample of 200 individuals, 4.5% of them work remotely. Find a 90% confidence interval for the true proportion of Americans that work remotely.

Suppose we estimated that 68 percent of Santa Fe students believe that black coffee is disgusting. If we wanted to know the true proportion of the students who share the same view at 99 percent confidence and 4.5 percent margin of error, how many people would we need to sample?

Suppose we want to estimate the proportion of college students who use stimulants to help them study. If we want to estimate this proportion to within 5% at the 95% confidence level, how many randomly selected college students must we survey?If we want to estimate this proportion to within 5% at the 90% confidence level, do we need to survey more students or can we survey fewer students (compared to your previous answer)? We need to survey more students or We can survey fewer students If we want to estimate this proportion to within 4% at the 95% confidence level, do we need to survey more students or can we survey fewer students (compared to your first answer)? We need to survey more students or We can survey fewer students

9. According to a poll, eighty seven percent (87%) of California adults (440 out of 506 surveyed) feel that education is one of the top issues facing California. We wish to construct a ninety percent (90%) confidence interval for the true proportion of California adults who feel that education is one of the top issues facing California.What is a point estimate for the true population proportion?

A dowser has correctly located water for a well 1 out of 2 times in Jones County. In Jones County, someone who is just guessing has a 40% chance of locating water for a well. Does this sample provide sufficient evidence that the dowser can locate water and is not just guessing?