At the movies: A movie theater is considering a showing of The Princess Bride for a 80's thowback night. In order to ensure the success of the evening, they've asked a random sample of 52 patrons whether they would come to the showing or not. Of the 52 patrons, 29 said that they would come to see the film. Construct a 95% confidence interval to determine the true proportion of all patrons who would be interested in attending the showing. a) What is the point estimate for the true proportion of interested patrons? (please input a proportion accurate to four decimal places) b) Complete the interpretation of the confidence interval. Please provide the bounds for the confidence interval in decimal form, accurate to four decimal places, and list the lower bound first. "We are % confident that the true proportion of patrons interested in attending the showing of The Princess Bride is between and c) The theater is only willing to show The Princess Bride if they are confident that at least 40% of their patrons would be interested in seeing the film. Should they show it? Yes Answer

A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=935 and x=561 who said "yes." Use a 95% confidence level.

When two births are randomly selected, the sample space for genders is bb, bg. gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is , and this is not affected by how many boys or girls have previously been born. 2 Determine the probabilities of each sample proportion. Probability Sample proportion of girls Tune intanare or cimnlifiad frartinne

For a class project, a political science student at a large university wants to estimate the percent of students who are registered voters. He surveys 500 students and finds that 300 are registered voters. Compute a 90% confidence interval for the true percent of students who are registered voters, and interpret the confidence interval.  Round your answer to nearest thousandth if necessary.    Interpret the result.