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A national grocer’s magazine reports the typical shopper spends 11.5 minutes in line waiting to check out. A sample of 19 shoppers at the local Farmer Jack’s showed a mean of 10.7 minutes with a standard deviation of 3.1 minutes. Is the waiting time at the local Farmer Jack’s less than that reported in the national magazine? Use the 0.050 significance level.

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Answer:

There is no significant evidence to support that waiting time is less than the mean reported.

Step-by-step explanation:

Given that :

Sample mean, x = 10.7

Standard deviation, s = 3.1

Sample, size , n = 19

H0: μ ≥ 11.5

H1: μ < 11.5

Using the t-test (sample size is small)

Test statistic :

(x - μ) / s/sqrt(n)

(10.7 - 11.5) / (3.1 / sqrt(19))

-0.8 / 0.7111887

= −1.124877

Tcritical = Tdf, 0.05

df = n - 1 ; T18,0.05/2 = - 2.101 (left tailed)

Decision region:

Reject H0 :

If Tstatistic < Tcritical

−1.124877 > - 2.101

Hence, We fail to reject H0

There is no significant evidence to support that waiting time is less than the mean reported.

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