Question

A sociologist claims that children spent more time watching television in 1981 than children do today. A study was conducted in 1981 to find the time that children watched television on weekdays.​ Recently, a similar study was conducted. The results of these studies​ (in hours per​ weekday) are shown below. Assume the population standard deviation is 0.7 for 1981 and 0.7 for today. At α=​0.05, can you support the​ sociologist's claim? Complete parts​ (a) through​ (d) below.

Full data set
1981	1.2	1.2	1.3	1.6	1.9	3.3	2.7	2.5	1.9	3.4	3.4	2.5	2.3	1.8	1.1
	2.5	1.6	2.6	1.7	1.9	2.5	2.7	1.3	2.8	2.2	1.6	1.6	1.3	1.2	1.8
RecentlyRecently	0.8	1.8	0.8	2.8	0.8	0.9	2.3	2.7	1.3	1.2	2.7	1.8	1.8	2.8	1.3
	3.1	2.9	2.5	2.1	1.9	2.1	2.5	1.9	2.1	1.5	1.2	2.4	1.8	2.8	3.2

​

A) identify the claim and state H₀ and H₀

B) find the critical value and identify the rejection region

C) find the standardized test statistic z,

D) decide whether to reject or fail to reject the null hypothesis

Answer 1

for 1981

= 2.047

for recent

= 1.993

A) Claim :

H₀: 

H₁: 

B) At alpha = 0.05, the critical value is z_0.95 = 1.645

Reject H₀ if z > 1.645

C) The test statistic z = ()/

= (2.047 - 1.993)/sqrt((0.7)^2/30 + (0.7)^2/30) = 0.30

D) since the test statistic value is not greater than the critical value (0.30 < 1.645), so we should not reject the null hypothesis.