Question

1. Conduct a descriptive data analysis that includes the following:
   1. a measure of central tendency
   2. a measure of dispersion
   3. at least one graph
2. Briefly interpret the descriptive data analysis.
3. Conduct the appropriate statistical test that will answer your hypothesis. It must be a statistical test covered in this course such as regression analysis, single t-test, independent t-test, cross-tabulations, Chi-square, or One-Way ANOVA. Explain your justification for using the test based on the type of data and the level of measurement.
4. Report and interpret your findings. Use APA style and include a statement about whether you reject or fail to reject the null hypothesis.

Daily Physical Activity	Very Little Daily Physical Activity
6	8
12	8
8	8
8	8
12	6
7	10
7	10
7	10
13	8
9	9
9	9
10	12
6	7
8	9
7	10
6	12
11	8
11	11
10	7
7	6
6	6
8	8
13	6
13	6
10	10
8	10
8	7
12	7
9	6
12	12

Answer 1

As the data size is more than 25, I can use statistical software in my work and here I have completed this work using Ms Excel . [If you want the solution by hand or in any other software, do comment; I shall help you with that]

Copy the data along with the labels starting from cell A1.

[STEPS: Go to data, select Data Analysis, select Descriptive statistics; give the input range as $A$1:$B$31, check the checkbox of labels in the first row, and group by columns, summary statistics , give the output range as $D$2 and click on OK]

Daily Physical Activity		Very Little Daily Physical Activity
Mean	9.1	Mean	8.466667
Standard Error	0.424399508	Standard Error	0.348175
Median	8.5	Median	8
Mode	8	Mode	8
Standard Deviation	2.32453184	Standard Deviation	1.907035
Sample Variance	5.403448276	Sample Variance	3.636782
Kurtosis	-1.186484583	Kurtosis	-0.82558
Skewness	0.346971251	Skewness	0.358501
Range	7	Range	6
Minimum	6	Minimum	6
Maximum	13	Maximum	12
Sum	273	Sum	254
Count	30	Count	30

[STEPS TO INSERT THE GRAPH: Select the data, go to Insert, click on Columns , select the first type and click on OK]

From the chart the following observations can be made:

• The mean of Daily Physical Activity is more than Very Little Daily Physical Activity.
• The standard error of Very Little Daily Physical Activity is low and hence it is more reliable.
• The median of Daily Physical Activity is a bit more and the mode are equal for both the variables.
• The variance as well as SD of Very Little Daily Physical Activity is lesser and hence it has less variability.
• Hence from all the measures, it is evident that the variability is low in Ver Little Daily Physical Activity.

Here the appropriate test will be if we test that Daily Physical Activity is better Very Little Daily Physical Activity . Let the significance level be the usual 0.05.

Let 1 be the mean of the Daily Physical Activity and 2 be the mean of the Very Little Daily Physical Activity. Then we are to test

We conduct two sample t test .

[STEPS: Go to Data option, select Data Analysis, select t test: Two sample assuming unequal variances, give the range of the first variable as $A$1:$A$31 and the range of the second variable as $B$1:$B$31 and check the checkbox of labels and the significance level of 0.05 and give the ouput range as $I$2. Click on OK]

	Daily Physical Activity	Very Little Daily Physical Activity
Mean	9.1	8.466666667
Variance	5.403448276	3.636781609
Observations	30	30
Hypothesized Mean Difference	0
df	56
t Stat	1.153727479
P(T<=t) one-tail	0.126756129
t Critical one-tail	1.672522303

Now the p-value is given by 0.449816. Now as the p-value is more than 0.05, we fail to reject the null hypothesis at 5% level of significance and hence we conclude that Daily Physical Activity and Very Little Daily Physical Activity do not differ significantly at 5% level of significance.

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.