Question

The credit scores for 12 randomly selected adults who are considered high risk borrowers before and two years after they attend a personal finance seminar are given below.

	Credit Score
Adult	Before Seminar	After Seminar
1	608	646
2	620	692
3	610	715
4	650	669
5	640	725
6	680	786
7	655	700
8	602	650
9	644	660
10	656	650
11	632	680
12	664	702

You will run a significance test to check if there is enough evidence to support the claim that the personal finance seminar helps adults increase their credit scores.

You’ll use α = 0.01 for significance test.

1. 1. Write out the null and alternative hypothesis associated with the research question.
2. 2. What type of statistical test will you use to answer the proposed research question? (Note: Is this a z-test or a t-test for independent or dependent samples)
3. 3. What is the critical value at the 0.01 level of significance? Be sure and include whether this critical value is a z or t value and, if appropriate, include the degrees of freedom associated with this statistical test.
4. 4. What is the standardized test statistic?
   5. At 0.01 significance level what decision should be made about the null hypothesis? In other words, should you reject or retain the null hypothesis?
   6. Provide a brief conclusion regarding your findings.
   7. Show your excel output

Answer 1

Result:

You will run a significance test to check if there is enough evidence to support the claim that the personal finance seminar helps adults increase their credit scores.

You’ll use α = 0.01 for significance test.

Write out the null and alternative hypothesis associated with the research question.

Let = mean of difference( before-after)

Ho: µ_d=0 H1: µ_d < 0

This is a lower tail test.

What type of statistical test will you use to answer the proposed research question? (Note: Is this a z-test or a t-test for independent or dependent samples)

t-test for dependent samples ( data are paired)

What is the critical value at the 0.01 level of significance? Be sure and include whether this critical value is a z or t value and, if appropriate, include the degrees of freedom associated with this statistical test.

        DF= 12-1=1

       Critical t at 0.01 level of significance = -2.7181

Reject Ho is calculated t > -2.7181

What is the standardized test statistic?

test statistic = -5.0731

At 0.01 significance level what decision should be made about the null hypothesis? In other words, should you reject or retain the null hypothesis?

Since test statistic = -5.0731 is less than critical t value -2.7181, we reject the null hypothesis.

Provide a brief conclusion regarding your findings.

There is enough evidence to support the claim that the personal finance seminar helps adults increase their credit scores.

Show your excel output (Excel Addon PHStat used )

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.01
Intermediate Calculations
Sample Size	12
DBar	-51.1667
Degrees of Freedom	11
SD	34.9385
Standard Error	10.0859
t Test Statistic	-5.0731
Lower-Tail Test
Lower Critical Value	-2.7181
p-Value	0.0002
Reject the null hypothesis