Question

# The manager of a grocery store has taken a random sample of 100 customers. The average...

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 4.9 minutes with a sample standard deviation of 0.5 minutes. Conduct a test to determine whether or not the mean waiting time of all customers is significantly more than 5 minutes.

Use a significance level of α = 0.01.

Here we have to test that

n = 100

Sample mean =

Sample standard deviation = s = 0.5

Here population standard deviation is not known so we will use here t test.

Test statistic:

t = -2

Test statistic = -2

Degrees of freedom = n - 1 = 99

alpha = 0.01

P value from excel using command:

=T.DIST.RT(2,99)

= 0.0241                        (Round to 4 decimal)

P value = 0.0241

Here P value = 0.0241 > alpha = 0.01

So we fail to reject null hypothesis H0.

Conclusion: There is not sufficient evidence to conclude that the mean waiting time of all customers is significantly more than 5 minutes.

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