Question

The response times of technicians of a large heating company follow a Normal distribution with a standard deviation of 10 minutes. A supervisor suspects that the mean response time has increased from the target of 30 minutes. He takes a random sample of 25 response times and calculates the sample mean response time to be 33.8 minutes. What is the value of the test statistic for the appropriate hypothesis test?

Answer 1

The value of z test statistics for the appropriate hypothesis test is 1.90.

Explanation:

We are given that the response times of technicians of a large heating company follow a Normal distribution with a standard deviation of 10 minutes.

He takes a random sample of 25 response times and calculates the sample mean response time to be 33.8 minutes.

Let
`\mu` = mean response time.

So, Null Hypothesis,
`H_0` :
`\mu` = 30 minutes {means that the mean response time is 30 minutes}

Alternate Hypothesis,
`H_A` :
`\mu` > 30 minutes {means that the mean response time has increased from the target of 30 minutes}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. =
`(\bar X-\mu)/((s)/(√(n) ) )` ~ N(0,1)

where,
`\bar X` = sample mean response time = 33.8 minutes

`\sigma` = population standard deviation = 10 minutes

n = sample of response times = 25

So, test statistics =
`(33.8-30)/((10)/(√(25) ) )`

= 1.90

Hence, the value of z test statistics for the appropriate hypothesis test is 1.90.