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

Question

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). Here are the relative percent differences for all men and women over the age of 70 in the sample.

The figure below shows output for the two-sample t test using Option 1. (This output is from CrunchIt! software, which does Option 1 without rounding or truncating the degrees of freedom.) Do men and women over 70 years old differ in their perceptions of life expectancy? Using the output in the figure below, write a summary in a sentence or two, including t, df, P, and a conclusion.

There is somewhat strong evidence that men and women differ in their views on their own longevity. (Enter your answers to two decimal places.)

a) In this study, men underestimated their average life expectancy by what percent?
b) In this study, women underestimated their average life expectancy by what percent?
c) If these samples can be viewed as SRSs, then under H0: 1 = 2,a difference in the sample means as great as the one observed is how many standard errors below expected?
d) A more extreme difference would have occurred by chance alone about what percent of the time under repeated sampling? (Enter your answer to three decimal places.)

Explanation / Answer

There is somewhat strong evidence that men and women differ in their views on their own longevity. (Enter your answers to two decimal places.)

a) In this study, men underestimated their average life expectancy by 19.5 percent.
b) In this study, women underestimated their average life expectancy by 12.71 percent.
c) If these samples can be viewed as SRSs, then under H0: 1 = 2,a difference in the sample means as great as the one observed is 2.177 standard errors below expected.
d) A more extreme difference would have occurred by chance alone about 5.281 percent of the time under repeated sampling.

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