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.
SOLUTION
H0: 82% of home-schooled students receive their education entirely at home,
12% attend school up to 9 hours per week, and 6% spend from 9 to 25 hours per
week at school.
H1: The proportions differ from those stated in the null hypothesis. (Claim)
C. V. = 5.991 d. f. = 2 α = 0.05
O E
50 0.82 (85) = 69.7
25 0.12 (85) = 10.2
10 0.06 (85) = 5.1
