Question

9 16
8 21
6 18
5 14
8 15
6 13
9 20
5 19
7 17

Using the table above answer the following questions: Please show all your work.
1. Conduct hypothesis test to verify if there is a significant relationship between X
and Y using the t test approach
b. Calculate confidence interval for B 1
2. Perform hypothesis test to verify if there is a significant relationship between X
and Y using the F test approach.

Answer 1

??? It is given which one is x or y. However, I am considering the first column as x and the second one as y

The test is performed in MS Excel and the following steps are used-

Regression in excel

I performed the analysis using basic commands in MS Excel and I am giving the steps to be followed-

1. Select the Data tab and choose the Data Analysis in the top right-hand corner

2. In the Data Analysis menu choose Regression and click OK

3. In the ‘Input Range’ box, select all the data in the columns you created, including the variable names

4. Check the ‘Labels in First Row’ box

5. In the ‘Output Range’ box, enter a cell range where Excel will place the output and click OK

6. If the p-value were less than 0.05, you would reject the null hypothesis that says the means of all categories are equal. If the p-value were greater than 0.05, then you would fail to reject the null.

Now the following results are obtained -

1. The above table shows that the p-value is not as significant as it grater than 0.05 (at 5%) using the t-test. There is no significant relationship between X and Y

2. The confidence interval for b1

The blue shaded number represent the confidence interval for b1

3. Using the F-test to asses the significance of the relationship.

Since the p-value (Significance F) is too high so at 5% we do not have enough evidence to conclude that the given linear relationship between x and y is significant.