Question

A sociologist claims that children ages 3​ - 12 spent more mean time watching television in 1981 than children ages 3​ - 12 do today. A study was conducted in 1981 and a similar study was recently conducted. At  

alphaα

​= 0.025, can you support the​ sociologist's claim?

Sample 1				Sample 2
1981 Study	2.5	2.1	2.3	Recent Study	1.9	2.0	1.6
	1.6	2.6	2.1		1.5	2.1	2.3
	2.2	1.0	1.9		1.6	1.8	0.9

Calculate the Test Statistic and​ P-value.

Test Statistic

chi 2χ2

​= nothing

​P-value p​ = nothing

Test result

​P-value  

nothing  

alphaα

A.Reject

Upper H 0H0.

B.Do not reject

Upper H 0H0.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂
Alternative hypothesis: u₁ > u₂

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.025. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = 0.2129
DF = 16

t = [ (x₁ - x₂) - d ] / SE

t = 1.36

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is thesize of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 1.36.

P-value = P(t > 1.36)

Use the t-calculator to determine the p-value.

P-value = 0.096.

Interpret results. Since the P-value (0.096) is greater than the significance level (0.025), we cannot reject the null hypothesis.

Do not reject H0.

From the above test we do not have sufficient evidence in the favor of the claim that children ages 3​ - 12 spent more mean time watching television in 1981 than children ages 3​ - 12 do today.