Question

A random sample of *n*_{1} = 150 people ages 16
to 19 were taken from the island of Oahu, Hawaii, and 14 were found
to be high school dropouts. Another random sample of
*n*_{2} = 137people ages 16 to 19 were taken from
Sweetwater County, Wyoming, and 5 were found to be high school
dropouts. Do these data indicate that the population proportion of
high school dropouts on Oahu is different (either way) from that of
Sweetwater County? Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *p*_{1} =
*p*_{2}; *H*_{1}:
*p*_{1} <
*p*_{2}*H*_{0}:
*p*_{1} = *p*_{2};
*H*_{1}: *p*_{1} ≠
*p*_{2} *H*_{0}:
*p*_{1} ≠ *p*_{2};
*H*_{1}: *p*_{1} =
*p*_{2}*H*_{0}:
*p*_{1} = *p*_{2};
*H*_{1}: *p*_{1} >
*p*_{2}

(b) What sampling distribution will you use? What assumptions are
you making?

The standard normal. The number of trials is sufficiently
large.The Student's *t*. The number of trials is
sufficiently large. The standard
normal. We assume the population distributions are approximately
normal.The Student's *t*. We assume the population
distributions are approximately normal.

What is the value of the sample test statistic? (Test the
difference *p*_{1} − *p*_{2}. Do not
use rounded values. Round your final answer to two decimal
places.)

(c) Find (or estimate) the *P*-value. (Round your answer to
four decimal places.)

Sketch the sampling distribution and show the area corresponding to
the *P*-value.

(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis? Are the data statistically
significant at level *α*?

At the *α* = 0.01 level, we reject the null hypothesis
and conclude the data are not statistically significant.At the
*α* = 0.01 level, we fail to reject the null hypothesis and
conclude the data are statistically
significant. At the *α* = 0.01
level, we reject the null hypothesis and conclude the data are
statistically significant.At the *α* = 0.01 level, we fail
to reject the null hypothesis and conclude the data are not
statistically significant.

(e) Interpret your conclusion in the context of the
application.

Reject the null hypothesis, there is sufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.Fail to reject the null hypothesis, there is insufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County. Fail to reject the null hypothesis, there is sufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.Reject the null hypothesis, there is insufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.

Answer #1

Sociologists wish to determine if the high school drop out rate
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Hawii. Using a 1% level of significance, they determined that they
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of this conclusion.
At the 1% level of significance, it appears that the population
proportion of high school dropouts in Oahu is higher than that in
Sweetwater County.
At the 1% level of significance, it appears that the...

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