Question

2. Suppose the waiting time at the hospital follows a normal distribution. An
investigator randomly sampled 49 patients and found an average waiting time of
15 minutes and a standard deviation of 7 minutes. At the 1% significance level,
can we conclude that the mean waiting time is less than 17 minutes?
A. Specify the null and alternative hypotheses.
B. Determine the rejection region.
C. Calculate the test statistics.
D. Make a decision regarding the null hypothesis.
E. Report the conclusion.

Answer 1

A)
Null hypothesis, ho: the mean waiting time is equal to 17 minutes. u = 17
Alternative hypothesis, h1: the mean waiting time is less than 17 minutes. u < 17

B)
critical value, -z(a) = -z(0.05) = -1.645
Reject Null hypothesis if -z < -1.645

C)
test statistic, z = (mean-u)/(sd/sqrt(n))
z = (15-17)/(7/sqrt(49))
z = -2

D)
Since -z < -z(a), i reject the null hypothesis at 5% level of significance

E)
There is sufficient evidence to conclude that the mean waiting time is less than 17 minutes. u < 17