Please all the parts THX! 4. Below is a scatterplot and regression print-out rec

Question

Please all the parts THX!

4. Below is a scatterplot and regression print-out recording the ages of husband/wife pairs for country X (an unknown place on Earth) 60 rror t value 40 ntercept age husband 0.9112 0.0259 35.25 0.0000 20 20 40 60 Husband's age (in years) a. Before looking at the data, a friend of yours makes the claim that husbands in country X tend to be twice as old as their wives. Naturally, you disagree. Frame these claims in terms of hypotheses about the linear regression model. b. Make a decision about your hypotheses from part a using the printout. c. In the table, what value would your friend need to change 35.25 to if he wanted the number 0.0000 to change to 0.06 (and hence, win the argument)?

Explanation / Answer

a. We will frame the following hypothesis:

Ho: Husbands in country X are twice as old as their wives or the slope of the regression line is less than/equal to 0.5

H1: Husbands in country X are not twice as old as their wives or the slope of the regression line is more than 0.5

b. As the corresponding P-value for t=35.25 comes out to be 0.0000, we reject the null hypothesis. Therefore, the slope of the regression line is more than 0.5.

c. If we see the t-table, we have to change the value of t to get p=0.06. The value of t should be changed from 35.25 to 1.56, then the friend will win the argument because p>0.05 here.

d. According to the model equation,

y = 0.91x + 1.57

Here y = wife's age

x= husband's age = 38

Therefore, y = 0.91*38 + 1.57 = 36 years

So the model predicts that the husband age is 36 years

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