Homework Soursen a study of pregnant women and their ability to correctly p
n a study of pregnant women and their ability to correctly predict the sex of their baby,
57
of the pregnant women had 12 years of education or less, and
38.6%
of them correctly predicted the sex of their baby. Use a
0.01
significance level to test the claim that these women have no ability to predict the sex of their baby, and the results are not significantly different from those that would be expected with random guesses. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
Identify the null and alternative hypotheses. Choose the correct answer below.
A.
H0:
pequals=0.5
H1:
pless than<0.5
B.
H0:
pequals=0.5
H1:
pgreater than>0.5
C.
H0:
pequals=0.386
H1:
pgreater than>0.386
D.
H0:
pequals=0.386
H1:
pless than<0.386
E.
H0:
pequals=0.5
H1:
pnot equals0.5
F.
H0:
pequals=0.386
H1:
pnot equals0.386
The test statistic is
zequals=nothing.
(Round to two decimal places as needed.)The P-value is
nothing.
(Round to four decimal places as needed.)
Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.
Reject
Fail to reject
H0.
There
is not
is
sufficient evidence to warrant rejection of the claim that these women have no ability to predict the sex of their baby. The results for these women with 12 years of education or less suggests that their percentage of correct predictions
is
is not
very different from results expected with random guesses.
Solution
1.
Formulating the null and alternatuve hypotheses,
Ho: p = 0.5
Ha: p =/= 0.5 [ANSWER, OPTION E]
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2.
As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
p^ = x / n = 0.386
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.066226618
Getting the z statistic,
z = (p^ - po)/sp = -1.72 [ANSWER, TEST STATISTIC]
*****************************
3.
As this is a 2 tailed test, then, getting the p value,
p = 0.0854 [ANSWER]
*************************
4.
As P > 0.01, we FAIL TO REJECT HO. [ANSWER]
There IS NOT [ANSWER] sufficient evidence to warrant rejection of the claim that these women have no ability to predict the sex of their baby.
The results for these women with 12 years of education or less suggests that their percentage of correct predictions IS NOT [ANSWER] very different from results expected with random guesses.
