Question

You are required to show all work, which will include completing the following steps:

1. Determine your null and alternative hypotheses (see Slide 11)
2. Set up a table (see Slide 10)Compute the estimated variance of the difference scores (see Slide 14)
3. Compute the standard error of the mean difference (see Slide 15)
4. Compute the t obtained (see Slide 16)
5. Identify the t critical using the charts provided in class (see Slide 17)
6. Compare the t obtained to the t critical to determine if the t obtained falls within the region of rejection (see Slide 18)
7. Determine whether to accept or reject the null hypothesis

data set 1

14,14,13,13,10,12,14,15,17

data set 2

15,16,15,16,14,13,18,17,19

Answer 1

Following are the steps to perform the hypothesis:

Step 1: Hypothesis

Null Hypothesis: Ho: u₁ is equal to u₂

Alternate Hypothesis: Ha: u₁ is not equal to u₂

Step 2: Decide the level of significance

The level of significance is assumed to be 0.05

Step 3: Following formula can be used to calculate the estimated variance

The standard deviation can be calculated by using (=stdev.s) command in excel:

Step 4: Standard Error

Step 5: t-statistic

The mean value can be calculated using (=average command) in excel

Step 6: Calculate the degrees of freedom

df = n₁ + n₂ - 2

df = 9 + 9 - 2 = 16

Step 7: the critical value

The critical value can be determined by t distribution table at df = 16 and 0.05 level of significance

Step 8: Conclusion

Since the t-critical value (2.12) is more than the calculated t-value (-2.57), the null hypothesis will be rejected.

There is enough evidence to indicate that there is significant difference between the mean value of two groups