Question

The following data show the average retirement ages for a random sample of workers in the United States and a random sample of workers in Japan. Perform a hypothesis test using α = 0.05 to determine if the average retirement age in Japan is different from the United States. Calculate the test-statistics (round to 3 decimals - report the absolute value).

Answer 1

`t \approx 2.639`

Explanation:

Given

`\begin{array}{ccc}{} & {USA\ 1} & {Japan\ 2} & {\bar x} & {64.6} & {67.5} &{n} & {30} & {30} & {\sigma} & {4.0} & {4.5} \ \end{array}`

See attachment for data

Required

Determine the test statistic

The test statistic is calculated using:

`t = \frac{\bar x_1 - \bar x_2}{\sqrt{(\sigma_1^2)/(n_1) + (\sigma_2^2)/(n_2)}}`

So, we have:

`t = \frac{64.6 - 67.5}{\sqrt{(4.0^2)/(30) + (4.5^2)/(30)}}`

`t = \frac{64.6 - 67.5}{\sqrt{(16.00)/(30) + (20.25)/(30)}}`

`t = \frac{64.6 - 67.5}{\sqrt{(16.00+20.25)/(30)}}`

`t = \frac{64.6 - 67.5}{\sqrt{(36.25)/(30)}}`

`t = (-2.9)/(√(1.2083))`

`t = (-2.9)/(1.099)`

`t \approx -2.639`

The absolute value is:

`t \approx 2.639`