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. (Data set may be foundhere.)

https://bcs.whfreeman.com/webpub/statistics/shared_resources/datasets_bridge/dataset_window.html?bps7e&ex21-08lifeexp

The figure below shows the output for the two-samplet-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, a summary in a sentence or two, includingt,df,P, and a conclusion.

Results - t 2-Sample X Export Null hypothesis: Difference of means = 0 Alternative hypothesis: Difference of means is not 0 Sex Std Dev Sample Mean |n M 5.612 -19.50 6 F 5.589 -12.71 7 df: 10.68 Difference of means: -6.786 t statistic: -2.177 P-value: 0.05281