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Chapter 9: Problem 69

A study claims that \(65 \%\) of students at all colleges and universities hold off-campus (part-time or full-time) jobs. You want to check if the percentage of students at your school who hold off-campus jobs is different from \(65 \%\). Briefly explain how you would conduct such a test. Collect data from 40 students at your school on whether or not they hold off-campus jobs. Then, calculate the proportion of students in this sample who hold off-campus jobs. Using this information, test the hypothesis. Select your own significance level.

Short Answer

Expert verified
The answer depends on the results of the hypothesis test, particularly the calculated Z value and the associated probability. Based on these, you will either reject or fail to reject the null hypothesis that the proportion of students at your school holding off-campus jobs is 65%.

Step by step solution

01

State the Hypotheses

For a hypothesis test, the first step is to state the null hypothesis (\(H_0\)) and alternative hypothesis (\(H_1\)). In this case, \(H_0\) is that the proportion of students at your school who hold off-campus jobs is 65%, or \(P=0.65\). The alternative hypothesis \(H_1\) is that the proportion is different from 65%, or \(P\neq0.65\).
02

Conduct a Survey

In order to test these hypotheses, data needs to be collected. For this, conduct a survey among 40 students at your school to find out if they hold off-campus jobs.
03

Calculate the Sample Proportion

Once the survey data is collected, calculate the sample proportion. This is done by dividing the number of students who hold off-campus jobs by the total number of students surveyed.
04

Perform a Hypothesis Test

Now, compare the sample proportion with the claimed proportion of 0.65 under the null hypothesis. Since no significance level is given, you are free to choose a standard one, like 0.05. Use a Z-test to determine the test statistic. The Z value will be calculated using the formula: \(Z = (\text{{sample proportion}} - \text{{population proportion}}) / \sqrt{((\text{{population proportion}})(1 - \text{{population proportion}}))/\text{{sample size}}}\)
05

Determine the Decision

Finally, look up the Z value in the Z-table to find the associated probability. If the probability is less than the chosen significance level, reject the null hypothesis. If it is greater, fail to reject the null hypothesis. This will be the conclusion of the hypothesis test.

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