Question

A nationwide survey in 1995 revealed that U.S. grade-school children spend an average of µ = 8.4 hours per week doing homework. The distribution is normal with σ = 3.2. Last year, a sample of n = 100 grade-school children was given the same survey. For this sample, the mean number of homework hours was 7.1. Has there been a significant change in the homework habits of grade-school children? Test with α = .05.

***Write out all steps of hypothesis testing including populations, hypotheses, cutoff scores, and all relevant calculations.

Answer 1

Solution:
Given in the question
Null hypothesis H0: µ = 8.4
Alternate hypothesis Ha: µ 8.4
Population standard deviation(σ) = 3.2
No. of sample n = 100
Sample mean = 7.1
Here we will use Z-test because the sample size is greater than 30 and the population standard deviation is known
So Ztest stat = (Xbar - µ)/σ/sqrt(100) = (7.1-8.4)/3.2/sqrt(100) = -1.3/0.32 = -4.06
At alpha = 0.05 and this is two-tailed test so Critical values are +/-1.96
And decision rules, if the test stat value is less than -1.96 or greater than 1.96 than reject Null hypothesis else do not reject the null hypothesis.
Here we can see that the Z-test stat value is less than -1.96 i.e. (-4.06<-1.96) so we can reject the null hypothesis. and we have a significant effect that there has been a significant prrof in the homework habits of grade school children.