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Do women and men differ in how they perceive their life expectancy?

A researcher asked a sample of men and women to indicate their life expectancy. This was compared with values from actuarial tables, and the relative percent difference was computed. Perceived life expectancy minus life expectancy from actuarial tables was divided by life expectancy from actuarial tables and converted to a percent.

The data given are the relative percent differences for all men and women over the age of 70 in the sample:

Men: -28, -24, -21, -22, -15, -13
Women: -22, -20, -17, -9, -10, -11, -6

Use technology to approximate the t distribution for this test. Do NOT use the conservative approach.

1. What is the test statistic \( t \)?
- (Enter your answer rounded to three decimal places.)

2. What is the degrees of freedom of the test statistic \( t \)?
- (Enter your answer rounded to three decimal places.)

Answer :

The test statistic for the relative percent differences in perceived life expectancy between men and women is -18.308, and the degrees of freedom for the test statistic are 12.

Let's calculate the test statistic, which is the mean of the relative percent differences for men and women combined:

Men: -28, -24, -21, -22, -15, -13

Women: -22, -20, -17, -9, -10, -11, -6

Combining the data:

-28, -24, -21, -22, -15, -13, -22, -20, -17, -9, -10, -11, -6

The mean of these values is (-28 - 24 - 21 - 22 - 15 - 13 - 22 - 20 - 17 - 9 - 10 - 11 - 6) / 13

= -18.308.

Next, we need to calculate the degrees of freedom for the test statistic. The degrees of freedom can be determined using the formula: df = n - 1, where n is the number of data points.

We have 13 data points, so the degrees of freedom are 13 - 1 = 12.

Therefore, the test statistic is -18.308 and the degrees of freedom are 12.

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