Question

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 your decision and why?

	A) Do not Reject since p-value > 0.05
	B) Reject since p-value > 0.05
	C) Do not Reject since p-value < 0.05
	D) Reject since p-value < 0.05
	E) Cannot determine with the information given.

Answer 1

$\mu _{1}$ : Average number binge drinks consumed by  lower incomes (below $75000) group

$\mu _{2}$ : Average number binge drinks consumed by  high incomes (above $75000) Group

Null hypothesis : H_o : $\mu _{1}$ =$\mu _{2}$ ; $\mu _{1}$ - $\mu _{2}$ =0

Alternate hypothesis : H_a: $\mu _{1}$ > $\mu _{2}$ ; $\mu _{1}$ - $\mu _{2}$ > 0

Right Tailed test.

Assumed unequal population variances :

Income Group	n	Average Number of Binge Drinks Per Year	Standard Deviation
Below $75000 (A)	n1= 22	$\overline{x}_{1}$ = 432	s1 = 25.16
$75000 and above (B)	n2=40	$\overline{x}_{2}$= 377	s2 = 22.18

Degrees of Freedom: A=1 [(sini) + (s/n2)? (/m) + (/. -1 + 12-1

[25.16 22) + (22.182 40) (25.16 22 1 (22.182/40) 2- 1 0 -1 (28.7739) + (12.298) _1686.9668 30.4256 +3.8785- 830 = 38.9563 x 38

D1 - 432 - 377) 55 Test Statistic: tstat = 6.4088 = 8.5819 V-212 +22.182

For right tailed test :

P -Value = P(t > tstat) = Plt > 8.5819)

for 38 degrees of freedom, P(t>8.5819) =0.0000

p-value = 0.0000

As P-Value i.e. is less than Level of significance i.e (P-value:0 < 0.05:Level of significance); Reject Null Hypothesis

Ans :

D)	Reject since p-value < 0.05