Waiting times for n = 105 people are independently observed. It was found that 25 peoplewaited less than 2 minutes, 30 people waited between 2 and 9 minutes, and 50 people waitedmore than 9 minutes. A manager is interested in testing whether waiting the time X isexponentially distributed. Recall that the exponential cdf is F(x) = 1 - e
-x/λ with mean λ.
(a) Under H0 that X is exponential, what is the estimated expected number of people towait less than 2 minutes? Between 2 and 9 minutes? More than 9 minutes?
(b) What is the chi-square test statistic for H0? What are the degrees of freedom?
(c) With a significance level of 0.05, what is the manager's conclusion?
In a study on desired heights, 50 randomly sampled college students were asked to reportactual height and ideal height. The difference between the two variables (ideal minus actual)was also recorded. Summary statistics are shown in the table below.mean stddev
actual 63.1 4.1
ideal 65.6 3.9
difference 2.5 2.2
Is there significant evidence that all college students would on average rather be taller? Answer
with the appropriate hypothesis test with α = .05.