1. Do the percentages of on-time arrivals differ between airlines? Two major airlines , Airline M and Airline F were sur

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1. Do the percentages of on-time arrivals differ betweenairlines? Two major airlines , Airline M and Airline F weresurveyed. Flights were randomly and independently selected fromeach airline. nm = 600 flights from Airline M were examined. Ofthese, xm = 426 flights were on-time. nf = 500 flights from AirlineF were examined. Of these, xf = 370 flights were on-time.Suppose pm is the true proportion of flightsfrom Airline M which are on-time.Suppose pf is the true proportion flights fromAirline F which areon-time. pm and pf areunknown and we will examine relations between them based upon thesesamples. Let pmhat be the sample proportion of flights from AirlineM which were on-time. Let pfhat be the sample proportion of flightsfrom Airline F which were on-time.
a)Calculate an unbiased point estimateof pm.
b) We wish to construct a 95 % classical confidence intervalfor pm. What is the critical value multiplierzstar?
c) Create a 95% classical confidence intervalfor pm? ( _______ , _______)
d) How long is the 95% classical confidence intervalfor pm?
e) In terms of pm = p and nm = n, give theformula for the standard deviation of the distribution of thesample proportion pmhat.(R code)
(a) p*(1-p)/n
(b) n*p*(1-p)
(c) sqrt(n*p*(1-p))
(d) sqrt(p*(1-p)/n)
f) Calculate an unbiased point estimateof pf
g) Calculate an unbiased point estimateof pm - pf
h)Based on this data, calculate a 95% classical confidenceinterval for pm - pf. ( _____, _____)
i. How long is the 95% classical confidence intervalfor pm - pf calculatedabove?
j) Copy your R script for the above into the text box here.