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

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.

write out all the steps of hypothesis testing including
populations, hypotheses, cutoff scores, and all relevant
calculations.
Nationwide survey in 92' showed US middle school students spend
u=8.4 hours doing homework. Distribution is normal o=3.2. Previous
year 100 middle school students and the mean of their homework time
was 7.1. Was there a significant change in homework times.Test
through a=.05
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