Students who are home-schooled often attend their local schools to participate in various types of activities such as sports or musical ensembles. According to the government, 82% of home-schoolers receive their education entirely at home, while 12% attend school up to 9 hours per week and 6% spend from 9 to 25 hours per week at school. A survey of 85 students who are home-schooled revealed the following information about where they receive their education.

At α = 0.05, is there sufficient evidence to conclude that the proportions differ from those stated by the government?
Perform these steps.
a. State the hypotheses and identify the claim.
b. Find the critical value.
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified.

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Entirely at home 50 Up to 9 hours 25 9 to 25 hours 10