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

[answerhappygod]

Do the percentages of on-time arrivals differ between airlines?Two major airlines , Airline M and Airline F were surveyed. Flightswere randomly and independently selected from each airline. nm =600 flights from Airline M were examined. Of these, xm = 426flights were on-time. nf = 500 flights from Airline F wereexamined. Of these, xf = 370 flights were on-time.Suppose
pm
is the true proportion of flights from Airline M which areon-time. Suppose
pf
is the true proportion flights from Airline F which areon-time.
pm
and
pf
are unknown and we will examine relations between thembased upon these samples. Let pmhat be the sample proportion offlights from Airline M which were on-time. Let pfhat be the sampleproportion 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 intervalfor
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 standarddeviation of the distribution of the sample proportion pmhat.(Rcode)
n*p*(1-p)p*(1-p)/n sqrt(n*p*(1-p))sqrt(p*(1-p)/n)
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 intervalfor
pm - pf
.
,
i. How long is the 95% classical confidence interval for
pm - pf
calculated above?