Question

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

Answer 1

`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`