Question

A study was done to investigate what people think is "creepy." Each person in a sample of women and a sample of men were asked to do the following.

Imagine a close friend of yours whose judgment you trust. Now imagine that this friend tells you that she or he just met someone for the first time and tells you that the person was creepy.

The people in the samples were then asked whether they thought the creepy person was more likely to be a male or a female. Of the 1,029 women surveyed, 980 said they thought it was more likely the creepy person was male, and 298 of the 312 men surveyed said they thought it was more likely the creepy person was male.

Is there convincing evidence that the proportion of women who
think the creepy person is more likely to be male is different from
this proportion for men? For purposes of this exercise, you can
assume that the samples are representative of the population of
adult women and the population of adult men. Test the appropriate
hypotheses using a significance level of 0.05. (Let
*p*_{1} be the proportion of women who think the
creepy person is more likely to be male, and *p*_{2}
be the proportion of men who think the creepy person is more likely
to be male.)

State the appropriate null and alternative hypotheses.

*H*_{0}: *p*_{1}
− *p*_{2} = 0

*H*_{a}:
*p*_{1} − *p*_{2} ≠
0

*H*_{0}: *p*_{1}
− *p*_{2} > 0

*H*_{a}:
*p*_{1} − *p*_{2}
< 0

*H*_{0}: *p*_{1}
− *p*_{2} < 0

*H*_{a}:
*p*_{1} − *p*_{2}
> 0

*H*_{0}: *p*_{1}
− *p*_{2} = 0

*H*_{a}:
*p*_{1} − *p*_{2}
> 0

*H*_{0}: *p*_{1}
− *p*_{2} = 0

*H*_{a}:
*p*_{1} − *p*_{2}
< 0

Find the test statistic and *P*-value. (Use a table or
technology. Round your test statistic to two decimal places and
your *P*-value to four decimal places.)

*z*=

*P*-value=

State the conclusion in the problem context.

We fail to reject *H*_{0}. We do not have
convincing evidence that the proportion of women who think the
creepy person is more likely to be male is different from this
proportion for men.

We reject *H*_{0}. We do not have convincing
evidence that the proportion of women who think the creepy person
is more likely to be male is different from this proportion for
men.

We reject *H*_{0}. We have convincing evidence
that the proportion of women who think the creepy person is more
likely to be male is different from this proportion for men.

We fail to reject *H*_{0}. We have convincing
evidence that the proportion of women who think the creepy person
is more likely to be male is different from this proportion for
men.

Answer #1

The statistical software output for this problem is:

Hence,

*H*_{0}: *p*_{1}
− *p*_{2} = 0

*H*_{a}:
*p*_{1} − *p*_{2} ≠
0

z = -0.20

P - value = 0.8408

Conclusion: We fail to reject *H*_{0}. We do not
have convincing evidence that the proportion of women who think the
creepy person is more likely to be male is different from this
proportion for men. **Option A** is correct.

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