Successful hotel managers must have personality characteristics often thought of

Question

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 _= 5.29. The mean score for the general male population is = 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 = 0.78 for the adult male population.

Step 1:

Fill in the blank: The z test statistic for the femininity score

for male hotel managers is ____. (Give your answer to two decimal places.)

Step 2:

Fill in the blank: The P-value for your z is ____. (Give your answer to 4 decimal places.)

Step 3:

Conclude: What is an appropriate conclusion for your test? Use = 0.05.

We do not reject the null hypothesis and conclude that hotel managers are different from other males in femininity, on average.

We reject the null hypothesis and conclude that hotel managers are different from other males in femininity, on average.

We reject the null hypothesis and conclude that hotel managers are similar to other males in femininity, on average.

We do not reject the null hypothesis and conclude that hotel managers are similar to other males in femininity, on average.

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 _= 5.29. The mean score for the general male population is = 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 = 0.78 for the adult male population.

Step 1:

Fill in the blank: The z test statistic for the femininity score

for male hotel managers is ____. (Give your answer to two decimal places.)

Step 2:

Fill in the blank: The P-value for your z is ____. (Give your answer to 4 decimal places.)

Step 3:

Conclude: What is an appropriate conclusion for your test? Use = 0.05.

We do not reject the null hypothesis and conclude that hotel managers are different from other males in femininity, on average.

We reject the null hypothesis and conclude that hotel managers are different from other males in femininity, on average.

We reject the null hypothesis and conclude that hotel managers are similar to other males in femininity, on average.

We do not reject the null hypothesis and conclude that hotel managers are similar to other males in femininity, on average.

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu = 5.19 vs H1 : mu 5.19

mu is the population mean.

Assume alpha = level of significance = 5% = 0.05

Here population standard deviation is known.

So we use Z-test.

The test statistic is,

Z = (Xbar - mu) / (/sqrt(n))

where Xbar is sample mean = 5.29

mu = 5.19

= population standard deviation = 0.78

n = sample size = 148

Z = (5.29 - 5.19) / (0.78/sqrt(148))

Z = 1.56

Now we have to find P-value.

P-value we can find by using EXCEL.

syntax is

=NORMSDIST(z)

where z is test statistic value.

P-value = 0.9406

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : We do not reject the null hypothesis and conclude that hotel managers are similar to other males in femininity, on average.

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