Parent groups in Independent Schools are concerned about the number of hours chi

Question

Parent groups in Independent Schools are concerned about the number of hours children are spending on homework each week. They are concerned that their children in middle school are being overloaded with homework (above the recommended level). The number of hours to be spent on homework in middle school (Years 8 to 9) recommended by DETA (Department of Education, Training and the Arts) is not more than 6 hours per week. To investigate parent concerns, a random sample of 20 Year 8 and 9 students were surveyed about the time spent on homework each week. The time spent on homework each week (in hours) is recorded below Studen 23 4567 8910 Homework 6.2 5.8 6.6 6.5 5.96.9 7.0 5.9 6.7 6.8 Student 112 13 1415 161718 19 20 Homework 5.75.85.8 6.6 6.8 5.96.57.2 5.0 5.8 (a) State the n and alternative hypotheses for an appropriate non-parametric test using the correct parameter (b) Describe an appropriate rejection region to test the claim, and state the distribution of the test statistio.

Explanation / Answer

Null Hypothesis H0: Number of hour spent on homework in middle school is not more than 6 Hours per week M<= 6 Hours

Alternate Hypothesis Ha: Number of hour spent on homework in middle school is more than 6 Hours per week M> 6 Hours

We will use one sample sign test (non parametric ) = Parametric T T Test

from Sample Size = 20

Number of Negative values (More than 6.0) = 11

so For significance level alpha = 0.05

Reject region will be .

CBIN (- Ve N < x; 20; 0.5) < 0.05

the value of N = 15 for one sided sign test

so Ncritical = 15

rejection region N >= 15

so here N = 11 so we cannot reject the null hypothesis and can cnclude that Number of hour spent on homework in middle school is not more than 6 Hours per week

the distribution of test statistic is binomial distribution with n = 20 and p = 0.5

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