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:

[tex]t \approx 2.639[/tex]

Step-by-step explanation:

Given

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

See attachment for data

Required

Determine the test statistic

The test statistic is calculated using:

[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}[/tex]

So, we have:

[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{4.0^2}{30} + \frac{4.5^2}{30}}}[/tex]

[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{16.00}{30} + \frac{20.25}{30}}}[/tex]

[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{16.00+20.25}{30}}}[/tex]

[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{36.25}{30}}}[/tex]

[tex]t = \frac{-2.9}{\sqrt{1.2083}}[/tex]

[tex]t = \frac{-2.9}{1.099}[/tex]

[tex]t \approx -2.639[/tex]

The absolute value is:

[tex]t \approx 2.639[/tex]

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