How well does the number of beers a student drinks predict his or her blood alco
ID: 3229548 • Letter: H
Question
How well does the number of beers a student drinks predict his or her blood alcohol content? Sixteen student volunteers at a university drank a randomly assigned number of 12-ounce cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC). Here are the data: The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don't believe that number of drinks predicts blood alcohol well. (a) find the equation of the least-squares regression line for predicting blood alcohol from number of beers. (Round your answers to four decimal places.) y - 1 + 2 x what is r^2 for these data? r^2 = 3 % Briefly summarize what your data analysis shows. BAC decreases as beer consumption increases, and the relationship between BAC and beer consumption is strong. BAC increases as beer consumption increases, and the relationship between BAC and beer consumption is strong. BAC decreases as beer consumption Increases, and the relationship between BAC and beer consumption is weak. BAC increases as beer consumption increases, end the relationship between BAC and beer consumption is weak. (b) Is there significant evidence that drinking more beers alters blood alcohol on the average In the population of all students? State hypotheses, give a test statistic and P-value, and state your conclusion. (Round your value for t to three decimal places, and round your value for P to four decimal pieces.) Null Hypothesis: H_0; Drinking more beers Increases BAC. H_0: There Is no relationship between BAC and beer consumption. H_0: Drinking more beers decreases BAC. H_0: There is a relationship between BAC and beer consumption. Alternative hypothesis: H_a: There is no relationship between BAC and beer consumption. H_a: There is a relationship between BAC and beer consumption. H_a: Drinking more beers increases BAC. H_a: Drinking more beers decreases BAC. t = 7 p = 8 Conclusion We do not have enough evidence to conclude that drinking more beers increases BAC. We have enough evidence to conclude that drinking more beers increases BAC.Explanation / Answer
Answer:
a). y = -0.0145+0.0179x
r2 =81.8%
BAC increases as beer consumption increases, and the relation between BAC and beer consumption is strong.
b).
Ho: There is no relationship between BAC and beer consumption.
Ha: There is a relationship between BAC and beer consumption.
t=7.942
P=0.0000
We have enough evidence to conclude that drinking more beers increases BAC.
Regression Analysis
r²
0.818
n
16
r
0.905
k
1
Std. Error
0.019
Dep. Var.
BAC
ANOVA table
Source
SS
df
MS
F
p-value
Regression
0.0239
1
0.0239
63.08
1.49E-06
Residual
0.0053
14
0.0004
Total
0.0292
15
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
-0.0145
0.0121
-1.192
.2530
-0.0405
0.0116
bears
0.0179
0.0022
7.942
0.0000
0.0130
0.0227
Regression Analysis
r²
0.818
n
16
r
0.905
k
1
Std. Error
0.019
Dep. Var.
BAC
ANOVA table
Source
SS
df
MS
F
p-value
Regression
0.0239
1
0.0239
63.08
1.49E-06
Residual
0.0053
14
0.0004
Total
0.0292
15
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
-0.0145
0.0121
-1.192
.2530
-0.0405
0.0116
bears
0.0179
0.0022
7.942
0.0000
0.0130
0.0227
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