Round to 3 decimal

Do the percentages of on-time arrivals differ between airlines? Two major airlines , Airline M and Airline F were surveyed. Flights were randomly and independently selected from each airline. nm = 600 flights from Airline M were examined. Of these, xm = 426 flights were on-time. of = 500 flights from Airline F were examined. Of these, xf = 370 flights were on-time. Suppose Pm is the true proportion of flights from Airline M which are on-time. Suppose pf is the true proportion flights from Airline F which are on-time. Pm and pf are unknown and we will examine relations between them based upon these samples. Let pmhat be the sample proportion of flights from Airline M which were on-time. Let phat be the sample proportion of flights from Airline F which were on-time. a) Calculate an unbiased point estimate of Pm . b) We wish to construct a 95 % classical confidence interval for Pm . What is the critical value multiplier zstar? c) Create a 95% classical confidence interval for Pm? d) How long is the 95% classical confidence interval for Pm? e) In terms of Pm = p and nm.= n, give the formula for the standard deviation of the distribution of the sample proportion pmhat.(R code) O sqrt(p*(1-p)) O sart(n*p*(1-p)) O p*(1-p) O n*p*(1-p) f) Calculate an unbiased point estimate of Pf g) Calculate an unbiased point estimate of Pm - Pf h)Based on this data, calculate a 95% classical confidence interval for Pm - Pf . i. How long is the 95% classical confidence interval for Pm - Pf calculated above? j) Copy your R script for the above into the text box here