Ex 11.6.2

1. A student believe that no more than 20% of the students who finish a statistics course get

an A. A random sample of 100 students was taken. 24% of the students in the sample received

As. (Hint: Ho: p0.2 v.s. Ha: p>0.2).

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(a) What is the standardized test statistic?

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(b) Test the hypothesis at the 1% level of significance using

the standardized test statistic.

reject Ho
do not reject Ho

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(c) What is the p-value? (to 4 digits)

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(d) Test the hypothesis at the 10% level of significance using

the p-value.

reject Ho
do not reject Ho

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2. An official of a large national union claims that the fraction of women in the union

is not significantly different from 0.5. Using the sample information reported below,

carry out a test of this statement. Use a 0.05 level of significance.

Sample size
400
Women
168
Men
232

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(a) What is the standardized test statistic?

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(b) What is the conclusion?
reject Ho
do not reject Ho

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3. Consider the following hypothesis test: Ho: p0.8 v.s. Ha: p>0.8.

A sample of 400 provided a sample proportion of 0.853.

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(a) What is the standardized test statistic? (to 2 digits)

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(b) Test the hypothesis at the 5% level of significance using

the standardized test statistic.

reject Ho
do not reject Ho

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(c) What is the p-value? (to 3 digits)