Letpdenote the population proportion of years in which the daytime temperature in the Twin Cities on St. Patrick's Day (March 17) is below the freezing point.It is known that in 98 out of the most recent 120 years, the daytime temperature in the Twin Cities on March 17 was below the freezing point.Assume that this data represents a random sample from the population.

1.(5 points) Construct a 99% confidence interval forp.Remember to check the assumptions and interpret the confidence interval.

The following R output might be useful:

qt(0.01, df=119, lower=F) = 2.358, qt(0.005, df=119, lower=F) = 2.618 qt(0.01, df=120, lower=F) = 2.357, qt(0.005, df=120, lower=F) = 2.617 qnorm(0.01, lower=F) = 2.326,   qnorm(0.005, lower=F) = 2.575 

2.(2 points) Based on the confidence interval in question 1, can you conclude that the true population proportionpis above 70%?Explain.

For questions 3 and 4, consider the following information:

Let denote the population mean snowfall in the Twin Cities in March (in inches).Based on the data from the most recent 100 years, the sample mean snowfall in the Twin Cities in March wasx= 9.3 inches with a standard deviation ofs= 7.8 inches.The data is right-skewed but only contains three outliers.Assume that this data represents a random sample from the population.

The following R output might be useful:

qt(0.05, df= 99, lower=F) = 1.660, qt(0.025, df= 99, lower=F) = 1.984 qt(0.05, df=100, lower=F) = 1.659, qt(0.025, df=100, lower=F) = 1.983 qnorm(0.05, lower=F) = 1.645,   qnorm(0.025, lower=F) = 1.960 

3.(5 points) Construct a 95% confidence interval for .Remember to check the assumptions and interpret the confidence interval.

4.(3 points) What is the minimum required sample size needed, if we wish to be 95% confident that we can estimate within 0.8 inches of the true value?Use the sample standard deviation as an educated guess for , and use thez-distribution instead of thet-distribution.