3) Succesful hotel managers must have personality characteristics often thought

Question

3) Succesful 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 = 529 The mean score for the general male population is 5.19. Do hotel managers, on the average, differ statistically significantly in femininity score from men in general? Assume that the standard rs is the same as the = 0.78 for the adult male population. (a)State null and alternative hypotheses in terms of the mean femininity score for male hotel managers. (b)Find the z test statistic by hand. Show work. (c) What does that test statistic tell you? (d) What is the P-value for your z? Show work. (you can use the z-test on your calculator to check your answer, but show me you can do it 'by hand' (e) What do you conclude about male hotel managers?

Explanation / Answer

Given that,
population mean(u)=5.19
sample mean, x =5.29
standard deviation, s =0.78
number (n)=148
null, Ho: =5.19
alternate, H1: !=5.19
level of significance, = 0.05
from standard normal table, two tailed t /2 =1.9762
since our test is two-tailed
reject Ho, if to < -1.9762 OR if to > 1.9762
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =5.29-5.19/(0.78/sqrt(148))
to =1.56
| to | =1.56
critical value
the value of |t | with n-1 = 147 d.f is 1.9762
we got |to| =1.56 & | t | =1.9762
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 1.5597 ) = 0.121
hence value of p0.05 < 0.121,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: =5.19
alternate, H1: !=5.19
b.
test statistic: 1.56
c.
decision: do not reject Ho

d.
p-value: 0.121

e.
we have evidence that differ statistically
significantly in femininity score from men in general

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