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 conclusion in the context of the problem?

	A) We have evidence to show that the average amount of binge drinks consumed by binge drinkers with income level below $75000 is greater than those with income level of $75000 and above.
	B) We do not have evidence to show that the average amount of binge drinks consumed by binge drinkers with income level below $75000 is greater than those with income level of $75000 and above.
	C) We have evidence to show that the average amount of binge drinks consumed by binge drinkers with income level below $75000 is less than those with income level of $75000 and above.
	D) We do not have evidence to show that the average amount of binge drinks consumed by binge drinkers with income level below $75000 is less than those with income level of $75000 and above.
	E) We have evidence to show that the average amount of binge drinks consumed by binge drinkers with income level below $75000 is different from those with income level of $75000 and above.

Answer 1

Option A is correct.

We will use 2 sample t test for difference of means.

Prior to proceeding for the t test, we will first the test the hypothesis for equality of variance test.

Below is the minitab output for equality of variance test by F test. Assumption is made that both the population follows normal distribution.

From F test, P value (0.485) is > alpha (0.05), thus we fail to reject Null and say the both the population variances are equal.

Now proceeding for 2 sample t test assuming equal variance of the populations.

Since p value ( 0.000) is < alpha (0.05) , thus we reject Null hypothesis and conclude that data is sufficient to evident that average amount of binge drinks for lower incomes below 75000 is greater than those with incomes greater than 75000.

Pooled estimate of population variance (Sp^2) is calculated as weighted average of the sample variances where weights being the degree of freedom of each sample.

df of population 1 = 21, df of pop. 2 = 39

Standard error of difference of means is given by Sp * SQRT (1/n1 + 1/n2)

Test statistic is given by t = ((x1 bar - x2 bar) - (mu1 - mu2)Ho)/standard error of difference of means,

where (mu1 - mu2)Ho is hypothesized difference between the means of the populations.