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twistedhyperboles
12.02.2021 •
Mathematics
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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Ответ:
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.
Ответ: