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.

1981
3.2
1.4
2.4
3.1
2.3
3.1
3.4
2.3
1.1
2.1
3.4
2.8
2.1
2.3
1.1
3.4
1.9
3.4
2.2
1.3
1.7
2.6
2.2
1.8
3.2
2.5
3.1
3.1
2.3
2.1

Recently
1.6
1.2
3.1
3.2
2.6
1.3
2.6
2.7
2.5
2.8
2.3
1.9
2.4
2.7
1.5
1.4
0.9
2.6
1.9
1.9
1.4
1.9
3.3
1.7
2.6
1.9
2.7
0.9
2.9
2.6

(a) Identify the claim and state Ho and Ha What is the claim?

Let the data from 1981 be sample 1 and let the recent data be sample 2.

Identify Ho and Ha Ho: u1 ____u2 Ha: u1_____u2

B. Find the critical value(s) and identify the rejection region Critical value(s) =

Identify Rejection region =

(c) Find the standardized test statistic z.

(d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. _____Ho. There ____ enough evidence at the ____level of significance to ______ the sociologist's claim that children spent ______ amount of time watching television in 1981 than children do today.

Answer 1

Ans:

sample mean for 1981=2.43

sample mean for recent=2.1667

n1=n2=30

a)

$H_0:\mu_1 \leq \mu _2$

(claim)

Ha : μ1 > μ2

Ha is claim.

b)Right tailed test

critical z value=1.645

Reject H0,if z>1.645

c)

Test statistic:

z=(2.43-2.1667)/SQRT((0.7^2/30)+(0.7^2/30))

z=1.457

d)Fail to reject the null hypothesis.

There is not enough evidence at the 0.05 level of significance to support the sociologist's claim that children spent more amount of time watching television in 1981 than children do today.