Question

** Please use only RStudio and include code **

The mean arrival rate of flights at Philadelphia International Airport is 195 flights or less per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days, the arrival rate per day is given in the data vector below called flights. Air traffic control manager wants to test if there is sufficient evidence that arrival rate has increased.

flights <- c(210, 215, 200, 189, 200, 213, 202, 181, 197, 199,

193, 209, 215, 192, 179, 196, 225, 199, 196, 210,

199, 188, 174, 176, 202, 195, 195, 208, 222, 221)

a) Find sample mean and sample standard deviation of arrival rate using R functions mean() and sd().

b) Is this a left-tailed, right-tailed or two-tailed test? Formulate the null and alternative hypothesis.

c) What is the statistical decision at the significance level α = .01?

** Please use only RStudio and include code **

Answer 1

Here we use R-studio

#a)

flights <- c(210, 215, 200, 189, 200, 213, 202, 181, 197, 199,193, 209, 215, 192, 179, 196, 225, 199, 196, 210,199, 188, 174, 176, 202, 195, 195, 208, 222, 221)
m=mean(flights);m
#[1] 200
s=sd(flights);s
#[1] 13.19352

#b)
#Here the hypothesis test is right-tailed
#The Null and alternative Hypothesis are
#Ho:mu<=195
#Ha:mu>195
t.test(flights,mu=195,)
#One Sample t-test
#data: flights
#t = 2.0757, df = 29, p-value = 0.02345
#alternative hypothesis: true mean is greater than 195
#95 percent confidence interval:
# 195.9071 Inf
#sample estimates:
#mean of x
# 200
#c)

#Here p-value = 0.02345>alpha=0.01 then we fail to reject null hypothesis Ho
#There is not sufficient evidence that arrival rate has increased.