Question

In a Harris poll of 514 human resource professionals, 45.9% said that body piercings and tattoos were big
grooming red flags. A professor of personnel managements believes that fewer than half of all human resources
professionals would say that body piercings and tattoos were big grooming red flags. Use a significance level of
0.01 and 0.05
H0: _____ _____ ______
Ha: _____ _____ ______
a. Follow our procedure on page 2 of our Unit 3 Day 1 notes to bracket the claim, etc.
b. Which word or phrase in the claim determines the inequality in the alternative hypothesis:
_________________
c. Which word, phrase or symbol in the problem tells us that this problem involves a test for the proportion,
and not a mean? _______________________________________________
d. Fill in the hypothesis.
e. Explain why the number “45.9” does not appear in the hypothesis: _______________________
_____________________________________________________________________________________
f. The p-value is 0.032. Find the outcome of the test and write a plain English interpretation of the outcome
using both α = 0.01 and α = 0.05.

Answer 1

a. H0: proportion of personnel managements believes that half of all human resources says that body piercings and tattoos were big grooming red flags.

vs Ha: proportion of personnel managements believes that fewer than half of all human resources says that body piercings and tattoos were big grooming red flags.

i.e, H0: p = 0.5 vs Ha:p<0.5

b. In the alternative hypothesis we see that the p<0.5, indicates the inequality. In words, the phrase "fewer than half of all human resources" shows the inequality.

c. In the problem, we can observe that phrase, "out of 514 resource professionals, 45.9% said that body piercings and tattoos were big grooming red flags.." 45.9% is actually the proportion of such professionals and not the mean. The proportion has been calculated by dividing the no of resource professionals who said that body piercings and tattoos were big grooming red flags by 514 that gives us the proportion as 0.459 i.e, 0.459*100=45.9%.

d. The Hypotheses are :

H0: p = 0.5 vs Ha:p < 0.5

e. We are testing whether the proportion of personnel managements believes that fewer than half of all human resources says that body piercings and tattoos were big grooming red flags. Hence, we need to test whether p<0.5 and not the proportion 0.459 or 45.9%. In other words, 45.9% is the estimate of the proportion and not the proportion to be tested.

f. p-value =0.032 is > α=0.01, Hence we fail to reject the null hypothesis and conclude that proportion is 0.5 i.e, half of all human resources says that body piercings and tattoos were big grooming red flags.

p-value =0.032 is < α=0.05, Hence we reject the null hypothesis and conclude that proportion is < 0.5 i.e, fewer than half of all human resources says that body piercings and tattoos were big grooming red flags.