Question

A manager wishes to determine whether the mean queuing time during peak hours for customers at a grocery store has changed from the target average queuing time of 5mins.
The manager tests this by sampling n = 35 customers at random and recording their queuing time. The average value of the sample is calculated to be 6.29 mins and queuing times in the sample vary by a standard deviation of s = 2.21 mins.
The hypotheses being tested are:
H ₀: μ = 5
H _a: μ ≠ 5.
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 than  and 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 queuing time, μ, is different to 5 mins.

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

An estimate of the population mean is 6.29
The standard error is 2.21/sqrt(35) = 0.3736

The distribution is normal

test statistic

t = (x - mean)/se
= ( 6.29 - 5)/0.3736
= 3.4529

Testing at significance level α = 0.05, the rejection region is: t > 2.032 or t < -2.032

Since the test statistic (is in the rejection region, there
is evidence to reject the null hypothesis, H 0.

There is sufficient evidence to suggest that the average queuing time, μ, is different to 5 mins.

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