Americans, on average, watch 2.90 hours TV per day according to the most recent

Question

Americans, on average, watch 2.90 hours TV per day according to the most recent data. Do people watch less TV than before? Use you your GSS data file which has been taken in 2008 and test a hypothesis of no difference in watching TV today and in the past.  Note: “One-sample Statistics” and “one-sample test” tables attached.

Question :When I Split the file by gender for men and women separately, do these individuals watch less TV than before?  Explain the differences?

One-Sample Statistics

N=1036 Mean=3.09 Std. Deviation= 2.900 Std. Error Mean=.090

HOURS PER DAY WATCHING TV   

One-Sample Test                      
Test Value = 2.90   

t= 2.160 df= 1035 Sig. (2-tailed) = .031 Mean Difference =.195 95% Confidence Interval of difference= Lower .02 Upper= .37

HOURS PER DAY WATCHING TV

Respondents sex = male

N=454 Mean=3.19 Std error= .140 Std Deviation = 2.981

HOURS PER DAY WATCHING TV

Respondents sex = female

N=584 Mean = 3.02 Std. error = .117 Std Deviation= 2.837

HOURS PER DAY WATCHING TV

Explanation / Answer

Solution:

Decision for One sample test

Null hypothesis: = 2.90
Alternative hypothesis: 2.90

Significance level = 0.05

t = 2.160

D.F = 1035

P value = 0.015501

Since p value is less than the significance value(0.05), so we have to reject the null hypothesis.

From this we conclude that we have sufficient evidence in the favor of the claim that there is significant difference between the mean hours of watching Tv per day.

Hypothesis test for male

N = 454, Mean = 3.19, Std error = 0.140, Std Deviation = 2.981

Our claim is that means hours watching Tv has decreased i.e mean hours in 2008 are more than the recent mean hours watching Tv per day(2.90)

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

Null hypothesis: < 2.90

Alternative hypothesis: > 2.90

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

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

SE = s / sqrt(n)

S.E = 0.140

DF = n - 1 = 454 - 1

D.F = 453

t = (x - ) / SE

t = 2.07

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Here is the logic of the analysis: Given the alternative hypothesis ( > 2.90), we want to know whether the observed sample mean is small enough to cause us to reject the null hypothesis.

The observed sample mean produced a t statistic test statistic of 2.07. We use the t Distribution Calculator to find P(t > 2.07) = 0.0195

Thus the P-value in this analysis is 0.0195

Interpret results. Since the P-value (0.0195) is smaller than the significance level (0.05), we have to reject the null hypothesis.

From this we conclude that we have strong evidence in the favor of the claim that mean hours watching Tv has decreased i.e mean hours watching Tv per day are more than 2.90 in 2008 for males.

Hypothesis test for female

N = 584, Mean = 3.02, Std. error = 0.117, Std Deviation = 2.837

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

Null hypothesis: < 2.90

Alternative hypothesis: > 2.90

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

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

SE = s / sqrt(n)

S.E = 0.117

DF = n - 1 = 584 - 1

D.F = 583

t = (x - ) / SE

t = 1.03

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Here is the logic of the analysis: Given the alternative hypothesis ( > 2.90), we want to know whether the observed sample mean is small enough to cause us to reject the null hypothesis.

The observed sample mean produced a t statistic test statistic of 1.03. We use the t Distribution Calculator to find P(t > 1.03) = 0.1517

Thus the P-value in this analysis is 0.1517

Interpret results. Since the P-value (0.1517) is greater than the significance level (0.05), we have to accept the null hypothesis.

From this we can conclude that we do not have sufficient evidence in the favor of the claim that mean hours for watching T.v per day has decreased from 2008 for females.

For male we got the sufficient evidence that means hours of watching Tv per day has decreased however for females we do not have sufficient evidence in the favor of the claim that mean hours for watching T.v per day has decreased from 2008 for females.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.