_ Math533 statistics Revision.
Renee Williams
Course Project
B
a. The average (mean) sales per week exceeds 41.5 per salesperson.
Null Hypothesis H(o): µ ≤ 41.5 (meaning the sales per week are less than 41.5 per salesperson)
Alternative hypothesis H(a): µ > 41.5 (meaning the sales per week are greater than 41.5 per
salesperson). Test statistics is z. Rejection Region: z < 1.65 which correspond with a = 0.05
The P-value 0.022 is less than a = 0.05 so reject the null and accept the alternative.
Based on the hypothesis test we can affirm that the manager speculation is correct when we use
the alpha = 0.05. We are 95% confident that sales made were between 41.522 and 43.158 per
week.
b. The true population proportion of salespeople that received online training is less than
55%. Null Hypothesis: H(o): µ < 0.55, Alternative hypothesis H(a): µ ≠0.55. Test statistics z.
Rejection region is z > 1.65 which corresponds with a = 0.05. We cannot reject the null and we
cannot accept the alternative hypothesis because the population proportion is greater than 55%
at an alpha = 0.05. The P-value 0.157 is also greater than the alpha 0.05. We are 95% confident
that the population of salespeople that received online training is between 0.398321 and
0.601679 or (40 and 60).
c. The average (mean) number of calls made per week by salespeople that had no training is
less than 145. Null Hypothesis: H(o): µ < 145, Alternative hypothesis H(a): µ ≠ 145. Rejection
region is z < 1.65 which corresponds with a = 0.05. Based on the hypothesis test we can affirm
that the manager speculation is correct when we use alpha = 0.05. So we reject the null and
accept the alternative based on the P-value 0.000 being less than the alpha 0.05. We are 95%
confident that the mean number of calls made by salespeople with no training is between 36.049
and 38.151 calls.
d. The average (mean) time per call is greater than 15 minutes. Null Hypothesis: H(o): µ >
15, Alternative hypothesis H(a): µ ≠ 15. Rejection region is z < 1.65 which corresponds with a
=
0.05. Based on the hypothesis test we can affirm that the manager speculation is correct when
the alpha = 0.05. So we accept the null and reject the hypothesis test. Also the P-value is greater
than the alpha = 0.05 letting us know that the manager speculation is correct. We are 95%
confident that the mean time per call is between 14.862 and 15.820 minutes
