Question

The security department of a factory wants to know whether the true average time required by the night guard to walk his round is less than 20 minutes. In a random sample of 35 rounds, the night guard averaged 19.61 minutes while his rounds varied by a standard deviation of s = 1.3 minutes. Test, at significance level α = 0.05, whether there is evidence that the true average time it takes the night guard to walk his round is less than 20 minutes, by testing the hypotheses: H 0: μ = 20 mins H a: μ < 20 mins.

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= .

The P-value for this test is calculated to be (4 dec places) .

Since the P-value is (smaller/larger) than (2 dec places), there (is evidence/is no evidence) to reject the null hypothesis, H 0.

There (is sufficient/is insufficient) evidence to suggest that the true average time it takes the night guard to walk his round, μ, is less than 20 minutes.

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): .

Answer 1

To Test :-

H 0: μ = 20 mins

H a: μ < 20 mins.

Standard error =

Test Statistic :-


t = -1.7748

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

P value = P ( t > 1.7748 ) = 0.04244

Reject null hypothesis if P value < level of significance

P value = 0.0424 < 0.05, hence we reject null hypothesis

Conclusion :- Accept Alternative Hypothesis

H a: μ < 20 mins.

There ( is sufficient ) evidence to suggest that the true average time it takes the night guard to walk his round, μ, is less than 20 minutes.

Were any assumptions required in order for this inference to be valid?

b: Yes - the population distribution must be normally distributed.