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1.) Construct a 95% confidence interval for the estimate of hsGPA. 2.) Construct

ID: 2910012 • Letter: 1

Question

1.) Construct a 95% confidence interval for the estimate of hsGPA.

2.) Construct a 90% confidence interval for the estimate of ACT.

3.) Based on your confidence interval for ACT, is ACT significant at the 10 percent level? Explain your answer in one or two sentences.

You are trying to estimate the effects of skipping class on college GPA. You estimate the equation, and have the following results (the standard errors are in parentheses below the coefficient estimates.) ColGPA 378 (064) Variable hsGPA 048 ACT (.039) -231 skipped (.065) 1.05 (.58) 280 261 intercept Obs R-squared

Explanation / Answer

1.) Construct a 95% confidence interval for the estimate of hsGPA.

Let's find degrees of freedom

df = n - p

where n = number of observations = 280

p = number of parameters including intercept = 4

therefore df = 280 - 4 = 276

Formula of confidence iinterval is

estimate value +/- ME

Where ME = margin of error.

Formula of ME is :

ME = tc *SE(estimate)

tc = critical t value with level of confidence c

Therefore for two tailed , df = 276 and c = 0.95

tc = 1.969

SE( estimate) = 0.064

Plug these values in the formula of ME, so we get

ME = 1.969 * 0.064 = 0.126

Lower limit = 0.378 - 0.126 = 0.252

Upper limit = 0.378 + 0.126 = 0.504

So the 95% confidence interval for the estimate of hsGPA is (0.252 , 0.504 )

2.) Construct a 90% confidence interval for the estimate of ACT.

For df = 76, c = 0.90, and two tailed., the critical t value is

tc = 1.65

ME = tc * SE (estimate ) = 1.65* 0.039 = 0.064

Lower limit = 0.048 - 0.064 = 0.016

Upper limit = 0.048 + 0.064 = 0.112

So the 90% confidence interval for the estimate of ACT is (0.016, 0.112 )

3.) Based on your confidence interval for ACT, is ACT significant at the 10 percent level? Explain your answer in one or two sentences.

Yes, ACT is  significant at the 10 percent level. Because zero is no included in the 90% confidence interval for the estimate of ACT