Consumption of a large amount of alcohol is known to increas

Consumption of a large amount of alcohol is known to increase reaction time. To investigate the effects of small amounts of alcohol, reaction time was recorded for five individuals before and after 2 ounces of alcohol was consumed by each. Does the data below suggest that the consumption of 2 ounces of alcohol increases mean reaction time?

Assume we want to use a 0.05 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, with
supporting work.
(c) Determine the p-value. Show all work; writing the correct critical value, with
supporting work.
(d) Is there sufficient evidence to support the claim that the consumption of 2 ounces of
alcohol increases mean reaction time? Justify your conclusion.

Solution

Here the null hypothesis is,

H0 : µd = 0 Vs H1 :  µd > 0

where,  µd is the population mean difference.

This is paired t-test.

alpha = 0.05

The test statistic is,

t =  Xbar / [sd/sqrt(n) ]

where Xbar is the mean of difference (after - before).

sd is the standard error of difference.

n is numbe of data pairs = 5

Xbar = sum of differences / total number of observations

Xbar = 4 / 5 = 0.8

sd = sqrt [ (d-dbar)² / n-1 ]

sd = 6.8 / 4 = 1.3038

t = 0.8 / [1.3038 / sqrt(5)]

t = 1.3720

The P-value we can calculate by using EXCEL.

syntax :

=tdist(x, d.f., tails)

where x is the test statistic value.

d.f. = n-1 = 5 - 1 = 4

tails = 1

P-value = 0.1210

P-value > 0.05

Accept H0 at 5% level of significance.

There is not sufficient evidence to say that the consumption of 2 ounces of alcohol increases mean reaction time