Asurvey has been conducted to estimate the usage of high-speed internet in the local area. 167 households were surveyed and asked whether they used high-speed internet at their home. 111 households surveyed responded that they do have a high-speed internet connection at home.
a)calculate the margin of error for the 95% confidence interval for the proportion of households that have a high-speed internet connection. give your answer as a decimal to 3 decimal places. margin of error =b)calculate the 95% confidence interval for the proportion of households that have a high-speed internet connection. give your answers as decimals to 3 decimal places.≤ p ≤

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?