Question

The efficieny expert investigating the pit stop completion times collected information from a sample of n = 50 trial run pit stops and found the average time taken for these trials is 10.75 secs and that the times varied by a standard deviation of s = 2.5 secs.
Help the efficiency expert to test whether this shows evidence that the pit crew are completing the change in less than 12 secs, testing the hypotheses you selected in the previous question.
Complete the test by filling in the blanks in the following:

• An estimate of the population mean is .
• The standard error is .
• The distribution is  (examples: normal / t12 / chisquare4 / F5,6).

The test statistic has value TS=  .
Testing at significance level α = 0.05, the rejection region is:
(less/greater) than  (2 dec places).
Since the test statistic  (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H ₀.
There (is sufficient/is insufficient) evidence to suggest that the average time taken for the pit crew to complete the pit stop, μ, is less than 12 .

Were any assumptions required in order for this inference to be valid?
a: No - the Central Limit Theorem applies, which states the sampling distribution is normal for any population distribution.
b: Yes - the population distribution must be normally distributed.
Insert your choice (a or b):

The test statistic has value TS=  .
Testing at significance level α = 0.05, the rejection region is:
(less/greater) than  (2 dec places).
Since the test statistic  (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H ₀.

Answer 1

Given,

• An estimate of population mean is sample mean

Hence estimate of population mean is 10.75

• Standard error is

Therefore, standard error is 0.3535534

• Since, the sample is large (n>30), then according to the central limit theorem for large sample size the distribution of sample mean is approximately normally distributed with mean and variance .

Hence, the distribution is normal and we use z- test.

• Our hypothesis is,

• Test statistics:

Test statistics is -3.536

• We have given , and this is the problem of left tailed test (i.e. less than 12 secs), so the rejection region is in the left side. Critical value at 0.05 level of significance for left tailed test is -1.645

Since, the test statistics is in the rejection region, which is also evident from the above normal plot. Hence, null hypothesis is rejected.

• Conclusion: Since is rejected, therefore we concludee that there is sufficient evidence to suggest that the average time taken for the pit crew to complete the pit stop, μ, is less than 12 .