8. A psychologist obtained recordings of election-night acceptance speeches of s

Question

8. A psychologist obtained recordings of election-night acceptance speeches of seven newly elected representatives to the U.S. Congress and counted the number of minutes devoted to urban problems in these speeches. The four representatives from rural districts devoted 5, 0, 3, and 4 minutes to urban problems, and the three representatives from urban districts devoted 11, 11, and 14 minutes to urban problems. Using the .01 significance level, did the amount of time devoted to urban problems in the acceptance speech differ according to the type of district the representative represented?

A) What is the appropriate test for this data?

B) Conduct the appropriate hypothesis test. Only hand calculate if you choose a z-test and then follow the five steps of hypothesis testing and provide a drawing. Otherwise, use SPSS.

C) Give an interpretation of this data (one sentence conclusion of the hypothesis test that should be free of statistical jargon) and report the statistics in APA format.

D) Explain why the test you chose is the most appropriate.

Mrural = 3

Murban = 12

SSrural = 14

SSurban= 6

Mdifference = 6

SSdifference = 150

Difference = Urban – Rural

Explanation / Answer

A) What is the appropriate test for this data?

Answer:

Here, we have to use two sample t test for the population means for the given data.

B) Conduct the appropriate hypothesis test. Only hand calculate if you choose a z-test and then follow the five steps of hypothesis testing and provide a drawing. Otherwise, use SPSS.

Answer:

Here, we have to use the SPSS for the two sample t test which is given as below:

Group Statistics

Area

N

Mean

Std. Deviation

Std. Error Mean

Time

Rural

4

3.0000

2.16025

1.08012

Urban

3

12.0000

1.73205

1.00000

Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

Time

Equal variances assumed

.042

.846

-5.892

5

.002

-9.00000

1.52753

-12.92663

-5.07337

Equal variances not assumed

-6.114

4.922

.002

-9.00000

1.47196

-12.80182

-5.19818

For the given test, the p-value is given as 0.002 which is very less and it is less than the level of significance 0.01, so we reject the null hypothesis that there is no any significant difference between the average numbers of minutes devoted to urban problems in speeches by rural and urban representatives.

C) Give an interpretation of this data (one sentence conclusion of the hypothesis test that should be free of statistical jargon) and report the statistics in APA format.

Answer:

We conclude that there is sufficient evidence that there is a significant difference between the average numbers of minutes devoted to urban problems in speeches by rural and urban representatives.

D) Explain why the test you chose is the most appropriate.

Answer:

The above chosen two sample t test is most appropriate because the sample sizes used in the samples are very less and the values for the population standard deviations are not given, that’s why we use the two sample t test for the population mean. If we were given a population standard deviations with appropriate or adequate sample sizes then we would use the two sample z test instead of two sample t test for the population mean.

Group Statistics

Area

N

Mean

Std. Deviation

Std. Error Mean

Time

Rural

4

3.0000

2.16025

1.08012

Urban

3

12.0000

1.73205

1.00000

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