In a national study of American high school students in 2006, researchers asked

Question

In a national study of American high school students in 2006, researchers asked students whether they have cheated on a test in the past year.

1 and 2. State the appropriate null and alternative hypotheses for testing whether the proportion of male students who admit to cheating is higher than that of female students. Researchers found that 61.8% of the male students admitted to cheating, compared to 58.3% of female students.

3. What further information would you need in order to conduct the test?

4. What additional information would you ask about how the data were collected in order to check whether the technical conditions are met?

5. Suppose the technical conditions are met and the test statistic turns out to be z = 1.82. Summarize the conclusion that you would draw from this test.

Explanation / Answer

Let p1 = proportion of males who cheat

p2 = proportion of females who cheat

H0: p1=p2

Ha: p1>p2

(Right tailed test)

For further analysis, sample size of males and females are also required.

Then only we can find std error for difference and compare test statistic with critical value.

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2) If students are selected at random to ensure the sample is not biased and results would be right.

and sample size is at par with population size.(reasonable sample size taken)

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3) z=1.82

Then p value for one tailed =.03438.

The result is significant at p < 0.05

Since p <0.05 reject H0

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