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 Student 23 4 56789 10 Homework 6.2 5.8 6.6 6.55.96.97.0 5.9 6.7 6.8 Homework 5.7 5.8 5.8 6.6 6.85.9 6.5 7.2 5.0 5.8 (a) State the nmull and alternative hypotheses for an appropriate non-parametrie test (b) Describe an appropriate rejection region to test the claim, and state the distribution Student 11 12 13 1415 16 17 18 1920 using the correct parameter of the test statistioc

Explanation / Answer

a) The hypothesis is

H0 : The children in the middle age are not being overload with work , with work being not more than 6 hours per week

H1 : The children in the middle age arebeing overload with work , with work being more than 6 hours per week

b) as this is a non paramteric test , we can use wilcox test to analyse this in R

The R snippet is as

homework <- c(6.2,5.8,6.6,6.5,5.9,6.9,7,5.9,6.7,6.8,5.7,5.8,5.8,6.6,6.8,5.9,6.5,7.2,5,5.8)

# the test
wilcox.test(homework,mu=6 , alternative = "greater")

wilcox.test(homework,mu=6 , alternative = "greater")

   Wilcoxon signed rank test with continuity correction

data: homework
V = 152.5, p-value = 0.03929
alternative hypothesis: true location is greater than 6

as the p value is less than signficance level of 0.05 , hence we reject the null hypothesis in favor of alternate hypothesis to conclude that The children in the middle age arebeing overload with work , with work being more than 6 hours per week

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