Question

Suppose a computer manufacturer claims that their average customer support call wait time is 30 seconds. We believe this to be an exaggeration of their efficiency and we wish to test this at a 99% confidence level. A random sample of 50 phone calls yields an average waiting period of 45 seconds, with a standard deviation of 15 seconds. Set up and conduct a test of the hypothesis that µ = 30 seconds against an appropriate alternative hypothesis.

Answer 1

H0:Null Hypothesis:$\mu$ = 30

HA; Alternative Hypothesis: $\mu$ > 30

n = 50

$\bar{x}$ = 45

s = 15

SE = s/$\sqrt{n}$ = 15/$\sqrt{50}$ =2.1213

Test statistic is:
Z = ($\bar{x}$ - $\mu$ )/SE

= (45 -30)/2.1213 = 7.0711

$\alpha$ = 0.01

One tail right side test

From Table, critical value of Z = 2.33

Since the calculated value of Z is greater than critical value of Z, Reject H0.

Conclusion:

The data does not support the computer manfacturer's claim that their average customer support call wait time is 30 seconds.