Question

Suppose a consumer product researcher wanted to find out whether a highlighter did not last as long as the manufacturer's claim that their highlighters could write continuously for 14 hours. The manufacturer claim means that the population of all highlighters will have a mean writing time of 14 hours with a standard deviation of 2 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. Following are the summary statistics from the sample: mean = 12.5 hours, Test the hypothesis at the 5% significance level using the 5-step hypothesis testing procedure (show all steps). Round all values to 2 decimal places.

Answer 1

Ho:mu=14

Ha:mu<14

left tail z test

level of significance=alpha=0.05

test statistic :

Z=xbar-mu/sigma/sqrt(n)

Z=(12.5-14)/(2/sqrt(40))

Z=-4.74

p value in excel for given test statistic

=NORM.S.DIST((12.5-14)/(2/SQRT(40)),TRUE)

=

1.05072E-06

p=0.00

p<0.05

Reject null hypothesis

Accept Alternative Hypothesis.

There is sufficient statistical evidence at 5% level of significance to conclude that

that the highlighters wrote for less than 14 continuous hours