Question

A researcher would like to test whether or not people who have stocked up on a year’s supply of toilet paper are experiencing less stress during a statewide stay-at-home order. A statewide poll indicates that the average stress level for the general state population is 60.5 (with a standard deviation of 11.6) and is normally distributed. Using a random sample of 36 toilet paper hoarders that have a mean stress level of 54.7 (and a standard deviation of 10.3), test the researcher’s hypothesis using an alpha of .03

State the hypotheses for this study, Establish the rejection criteria for this study, Compute the test statistic, Does toilet-paper hoarding significantly relieve stress during a pandemic? Yes/no – explain how you reached your conclusion. - Regardless of your answer to the previous question, then compute the effect size for this study.

Answer 1

The null and alternative hypothesis

We shall use z test for mean ( as sample size > 30 and population standard deviation is known ), this is a left tailed test (as  the alternative hypothesis is

For , the critical value of z is

zc = - 1.89 ( from z table : area from - infinity to -1.89 is 0.03 )

Reject H0 if z < -1.89

Test statistic is

= -3.00

Since calculated z < -1.89

We reject the null hypothesis

YES , there is sufficient evidence to conclude that hoarders have mean stress level less than that of general population .

Cohen's d effect size is given by

effect size =

= ( 54.7-60.5)/11.6

= 0.5 ( we ignore the sign in effect size)

Note : The effect size is medium

Note : Cohen's d

small effect :0.2

medium effect : 0.5

large effect : 0.8

Note : Though sample standard deviation is given , we have not used it , as it is not apprpriate for z test .