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Imagine you wish to determine whether the mean number of hours worked per week by men in a sample differs from the 40-hour standard. Use the information below to calculate the value of the single-sample t statistic.

Range = 60
Min Value = 5
Max value = 65
Mean = 42.31
Variance =100.00
Standard deviation = 10.00
Sum = 1,227

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Answer:


t = 7.359

Explanation:

Given


Range = 60


Min = 5


Max = 65


\bar x = 42.31


\sigma^2 =100.00


\sigma = 10.00


\sum = 1227


n=40

Required

The t statistic

This is calculated using:


t = (\bar x - \mu)/(\sigma/\sqrt n)

Where


\mu \to Population mean


\mu = (\sum )/(n)


\sum = 1227 and
n=40


\mu = (1227)/(40)


\mu = 30.675

So, we have:


t = (\bar x - \mu)/(\sigma/\sqrt n)


t = (42.31 - 30.675)/(10/√(40))


t = (42.31 - 30.675)/(10/6.325)


t = (11.635)/(1.581)


t = 7.359

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