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-squaredExplanation / 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
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