Question

(17.32) Successful hotel managers must have personality characteristics often thought of as feminine (such as “compassionate”) as well as those often thought of as masculine (such as “forceful”). The Bem Sex-Role Inventory (BSRI) is a personality test that gives separate ratings for female and male stereotypes, both on a scale of 1 to 7. A sample of 148 male general managers of three-star and four-star hotels had mean BSRI femininity score x¯¯¯x¯ = 5.29. The mean score for the general male population is μμ = 5.19. Do hotel managers, on the average, differ significantly in femininity score from men in general? Assume that the standard deviation of scores in the population of all male hotel managers is the same as the σσ = 0.78 for the adult male population. Fill in the blank: The P-value for your z is ____. (Give your answer to 4 decimal places.)

Answer 1

Solution:

Given that Sample mean x̅ = 5.29, Standard deviation σ = 0.78
Test Hypothesis:
The null hypothesis is: H0: μ = 5.19
The alternative hypothesis is: Ha: μ ≠ 5.19

Standard error of mean SE = σ / √ n
= 0.78/√148
= 0.78/12.1655
= 0.0641
Standard error of mean 0.0641
z = (x̅- μ ) / SE
z = (5.29-5.19) / 0.0641
z = 1.5597
The z-value is: 1.56

The P-value is:
P( z > 1.56) + P( z < -1.56) = 0.0594+ 0.0594 = 0.1188

Decision Rule : Here , P value = 0.1188 > α = 0.05

Therefore , fail to reject Ho
Conclusion : Hence , there is not sufficient evidence to conclude that the hotel managers on the average differ significantly in femininity score from men in general