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

Answer:

$t \approx 2.639$

Step-by-step 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:

$t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$

So, we have:

$t = \frac{64.6 - 67.5}{\sqrt{\frac{4.0^2}{30} + \frac{4.5^2}{30}}}$

$t = \frac{64.6 - 67.5}{\sqrt{\frac{16.00}{30} + \frac{20.25}{30}}}$

$t = \frac{64.6 - 67.5}{\sqrt{\frac{16.00+20.25}{30}}}$

$t = \frac{64.6 - 67.5}{\sqrt{\frac{36.25}{30}}}$

$t = \frac{-2.9}{\sqrt{1.2083}}$

$t = \frac{-2.9}{1.099}$

$t \approx -2.639$

The absolute value is:

$t \approx 2.639$