# Sampling Method and P-Values

See the attached file.

A sociologist wanted to determine which academic subject high school students preferred. The hypotheses she wishes to test are:

Ho: The percentage of female high school students who prefer mathematics is equal to the percentage of male students who prefer mathematics.

H1: The percentage of female high school students who prefer mathematics is lower than the percentage of male students who prefer mathematics.

Of the 2500 high school students, 1105 were male and 1395 were female. The sociologist randomly selected 150 of the female high school students and 150 of the male high school students, and asked the 300 students what academic subject they prefer. Of the 150 female students, 20% preferred mathematics; of the 150 male students, 30% preferred mathematics.

a) What sampling method was used to select the 300 students?

b) Using your TI calculator with a seed value of 32, identify the label for the first 5 female students.

c) Suppose the p-value for these test is 0.03. Is the difference in percentages at a 5% level? Explain.

d) Suppose the p-value for this test is 0.03. Is the difference in percentages significant at a 1% level? Explain.

e) What is the overall (weighted) sample proportion of those that preferred mathematics?

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#### Solution Preview

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Question 4:

A sociologist wanted to determine which academic subject high school students preferred. The hypotheses she wishes to test are:

Ho: The percentage of female high school students who prefer mathematics is equal to the percentage of male students who prefer mathematics.

H1: The percentage of female high school students who prefer mathematics is lower than the percentage of male students who prefer mathematics.

Of the 2500 high school students, 1105 were male and 1395 were female. The sociologist randomly selected 150 of the female high school students and 150 of the male high school students, and asked the 300 students what academic subject they prefer. Of the 150 female students, 20% preferred ...

#### Solution Summary

This is a problem set concerning statistics, sampling methods, p-values and probabilities. Solutions and explanations are given for parts a, c, d, and e.