Question

OpenNote Intro to Statistics 3rd Edition, prob. 7.38 a) We might wonder, is the age difference between husbands and wives consistent across ages? If this were the case, then the slope parameter would be β1 = 1. Use the information above to evaluate if there is strong evidence that the difference in husband and wife ages differs for different ages. Below are the choices.

I got it wrong and know the last one is not correct but I have no idea which of the first 2 possible answers is correct and then why.

There is strong evidence because the 95% confidence interval for β1 is (0.86, 0.96), which does not include 1.

There is strong evidence because the intercept does not equal 0.

There is strong evidence because p-value = 0.0000 for age_husband.

There is strong evidence because p-value = 0.1730 > 0.05 for the intercept.

Answer 1

The confidence interval doesn't include zero, which means the value of is not zero which implies the relationship between age of husband and wife.

If the p-value > 0.05, then we cannot reject the null hypothesis which is = 0, so last option is incorrect.

Whether the confidence interval include 1 or not, it doesn't determine the evidence. because the interval which doesn't include 1 may have strong evidence or not. so first option is incorrect.

so second option is correct. i.e. There is strong evidence because the intercept does not equal 0.