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Question 3. Below is the output from fitting a linear regression in R using the data on the math and reading scores for n = 200 students who participated in the High School and Beyond Survey. Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 21.03816 2.58945 8.125 4.76e-14 * read 0.60515 0.04865 12.438 < 2e-16 * (a) Do the data provide strong evidence of a linear association between the reading and math scores? State the null and alternative hypothesis, and write your conclusion based on the p-value. (b) Calculate and interpret a 95% confidence interval for the slope parameter $\beta_1$. Question 4. In each of the following scenarios, determine whether the two groups are paired or independent. (a) A psychologist is studying whether a four-week sleep therapy program improves sleep quality. The average nightly sleep duration (in hours) of 40 randomly selected participants is recorded before and after the program. (b) A researcher investigates whether there is a difference in political attitudes between people living in urban and rural areas. Survey data are collected from two random samples of 100 residents from each region.

          Question 3. Below is the output from fitting a linear regression in R using the data on
the math and reading scores for n = 200 students who participated in the High School and
Beyond Survey.
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 21.03816 2.58945 8.125 4.76e-14 ***
read 0.60515 0.04865 12.438 < 2e-16 ***
(a) Do the data provide strong evidence of a linear association between the reading and
math scores? State the null and alternative hypothesis, and write your conclusion based
on the p-value.
(b) Calculate and interpret a 95% confidence interval for the slope parameter $\beta_1$.
Question 4. In each of the following scenarios, determine whether the two groups are paired
or independent.
(a) A psychologist is studying whether a four-week sleep therapy program
improves sleep quality. The average nightly sleep duration (in hours) of 40 randomly
selected participants is recorded before and after the program.
(b) A researcher investigates whether there is a difference in political attitudes
between people living in urban and rural areas. Survey data are collected from two
random samples of 100 residents from each region.

question 3 below is the output from fitting a linear regression in r using the data on the math and reading scores for n 200 students who participated in the high school and beyond survey co 51348

Added by Rebecca M.

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