Suppose that a researcher using data on class sizeCS and ave

Suppose that a researcher, using data on class size(CS) and average test scores from 100 third-grade classes, estimates the OLS regression

Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression TestScore = 567.2360+(-6.3438) x CS, R2-0.11, SER= 12.5 (22.2360) (2.0332) Construct a 95% confidence interval for 1, the regression slope coefficient. The 95% confidence interval for 1, the regression slope coefficient, is The t-statistic for the two-sided test of the null hypothesis Ho: 1-0 is (Round your response to our decimal places.) The p value for the two sided test of the null hypothesis Ho 1-0 is . (Round your response to our decimal places. Do you reject the null hypothesis at the 1% level? QA. Yes, because the t-statistic is less than 2.58. OB. No, because the p-value is greater than 0.01 OC. Yes, because the t-statistic is greater than 2.58. OD. Yes, because the p-value is less than 0.01 D D ). (Round your responses to two decimal places)

Solution

a.

Step1. First compute the margin of error as follows:

1. Calculate alpha:

            Here, it is 0.05 (1-95/100)

2. Calculate critical probability:

           

3. Calculate degrees of freedom.

           

4. Find the critical value from using cumulative probability (0.975) and degrees of freedom (98).

Here, it is 1.984.

5. Calculate margin of error (ME)=critical value*standard error

           

6. Calculate confidence interval.