1. How well does the number of beers a student drinks predict his or her blood a

Question

1. How well does the number of beers a student drinks predict his or her blood alcohol content? Sixteen student volunteers at Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC). The data are

_________________________________________________________________________

The students were equally divided between men and women and different in weight and usual drinking habits. Because of this variation, many students don't believe that number of drinks predicts blood alcohol well. To help answer some of these questions these data are loaded into StatCrunch. The output from different options in StatCrunch are shown

Simple linear regression results:

Dependent Variable:BAC

Independent Variable: Beers

BAC= -0.012700604+ 0.017963716 Beers

R( correlation coefficient)=0.8943

R-sq = 0.79984075

Estimate of error standard deviation: 0.020440951

Parameter estimates:

0

< 0.0001

Predicted values:

0.032208

8

0.00754723

6

1) let B1 be the true slpe of the regression line predicting BAC from the number of beers. What are the null and alternative hypotheses?

H0:

H1:

2) Is the slope significant ?

i) Yes

ii) No

3) Construct a 95% confidence interval for the true slope, B1.

_____________ < B1 < _____________________ (Round to 3 digits beyond decimal)

4) In context, interpret the 95% confidence interval for the true slope.

we are 95% confident that _______________________________________
_____________________________________________________________
____________________________________________________________

5) The predicted BAC for someone who consumed 2.5 beer is _________________(Round to 3 digits beyond decimal)

6) What is the 95% confidence interval for the mean predicted BAC of all students who consume 2.5 beers?

(__________________ , _____________________) (Round to 3 digits beyond decimal)

Explanation / Answer

1.

H0: Regression coefficient is zero

H1:Regression coefficient is not equal to zero

2. P-value = 0.0001 which is less than alpha 0.05,

So we reject H0.

Yes, there is significant

3.The 95% confidence interval for the true slope, B1 is

(0.017963761 +/- 2.14478*0.0024017035)= (0.012812,0.02312)

4.

We are 95% confident that the population regression coefficient is between 0.012812 and 0.02312

5. Predict vlaue of Y is 0.032208

6. 95% confidence interval for the mean (-0.014525568, 0.07894317)

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