a

The sample is random and has 64 patients which would constitute less than 10% of the total ER population. The sample size is at least 30. Therefore, we can be lenient with the skew although no information is provided regarding the skew.

b

H0: The average waiting time is 127 minutes.

HA: The average waiting time is not 127 minutes.

The z-score is first computed.

avg1 = 127
avg2 = 137.5

s = 39
n = 64

SE = s/sqrt(n)

z = (avg2 - avg1)/SE
z
## [1] 2.153846
pval = 1-pnorm(z)
pval
## [1] 0.01562612

The p-value here is less than the significance level. Therefore, the null hypothesis can be rejected. Yes. The change in the wait times is statistically significant because the average waiting time has increased over the past year.

c

Yes. It would change. The p-value is greater than the significance level of 0.01. This implies that we would fail to reject the null hypothesis.