Question

7.

The National Institute on Alcohol Abuse and Alcoholism defines binge drinking as a pattern of drinking that brings blood alcohol concentration (BAC) levels to 0.08g/dL. It is cited as the most common and deadly pattern of alcohol abuse in the country, which can cause many health problems such as alcohol poisoning, sudden infant death syndrome, and chronic diseases, to name a few. In the binge drinking fact sheet published by the Center for Disease Control and Prevention, the amount of binge drinks consumed per year by binge drinkers are greater among those with lower incomes (below $75000) and educational level. In order to verify if this claim is true, a random sample of binge drinkers from the two income groups were obtained, and the data are summarized in the table below:

Income Group	n	Average Number of Binge Drinks Per Year	Standard Deviation
Below $75000 (A)	22	432	25.16
$75000 and above (B)	40	377	22.18

Conduct a test of hypothesis at 5% level of significance to verify the claim.

What is the test statistic and the degrees of freedom (if applicable)?

Question 7 options:

	A) t = 2.9833, df=21
	B) t = 8.5820, df = 21
	C) t = 2.9833, df = 39
	D) t = 8.5820, df = 39
	E) z = 0.8738

8.

The National Institute on Alcohol Abuse and Alcoholism defines binge drinking as a pattern of drinking that brings blood alcohol concentration (BAC) levels to 0.08g/dL. It is cited as the most common and deadly pattern of alcohol abuse in the country, which can cause many health problems such as alcohol poisoning, sudden infant death syndrome, and chronic diseases, to name a few. In the binge drinking fact sheet published by the Center for Disease Control and Prevention, the amount of binge drinks consumed per year by binge drinkers are greater among those with lower incomes (below $75000) and educational level. In order to verify if this claim is true, a random sample of binge drinkers from the two income groups were obtained, and the data are summarized in the table below:

Income Group	n	Average Number of Binge Drinks Per Year	Standard Deviation
Below $75000 (A)	22	432	25.16
$75000 and above (B)	40	377	22.18

Conduct a test of hypothesis at 5% level of significance to verify the claim.

What is the p-value for the test?

Question 8 options:

	A) p-value < 0.002
	B)
	C)
	D)
	E) 0.1922

Answer 1

7.
Given that,
mean(x)=432
standard deviation , s.d1=25.16
number(n1)=22
y(mean)=377
standard deviation, s.d2 =22.18
number(n2)=40
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.08
since our test is two-tailed
reject Ho, if to < -2.08 OR if to > 2.08
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =432-377/sqrt((633.0256/22)+(491.9524/40))
to =8.5820
| to | =8.5820
critical value
the value of |t α| with min (n1-1, n2-1) i.e 21 d.f is 2.08
we got |to| = 8.58195 & | t α | = 2.08
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 8.582 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 8.5820
option:B
critical value: -2.08 , 2.08
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that random sample of binge drinkers from the two income groups were obtained,
8.
p value is less than 0.001
option:B