Respuesta :
Answer:
The value of z test statistics for the appropriate hypothesis test is 1.90.
Step-by-step 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 [tex]\mu[/tex] = mean response time.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30 minutes {means that the mean response time is 30 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 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. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean response time = 33.8 minutes
[tex]\sigma[/tex] = population standard deviation = 10 minutes
n = sample of response times = 25
So, test statistics = [tex]\frac{33.8-30}{\frac{10}{\sqrt{25} } }[/tex]
= 1.90
Hence, the value of z test statistics for the appropriate hypothesis test is 1.90.
