Question

Samsung claims that the average wait time for a customer calling the Samsung Care support line is 175 seconds. A simple random sample of 45 customers was selected, and their average wait time was found to be 187 seconds. Assume the population standard deviation of wait time is 50 seconds. Is there enough evidence to conclude that the average wait time for a customer calling the Samsung Care support line is more than 175 seconds? Use α = 0.01.

a) State the null and alternative hypotheses in the context of the question.

b) Calculate the value of the test statistic. Check the required condition(s) to validate the test statistic.

c) Find the p-value.

d) What conclusion can we draw?

Answer 1

Solution :

$\mu$= 175

$\bar x$ =187

$\sigma$ =50

n = 45

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$  = 175

H_a : $\mu$ >175

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (187-175) / 50 / $\sqrt$ 45

= 1.61

Test statistic = z = 1.61

P(z > 1.61 ) = 1 - P(z < 1.61 ) =  0.9463

P-value =0.0537

$\alpha$ = 0.01

P-value > $\alpha$

0.0537 > 0.01

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that