Question

? Kara Danvers (Supergirl) has always relied on her strength to win fights. But what happens when she meets an alien just as strong? Her sister is training her to be a more technical fighter so that Supergirl can meet any challenge. The data below record the significant strikes during randomly selected training sessions 6 months apart. Is Kara showing improvement in her fighting?

Strikes (pre):	29	32	44	34	19
Strikes (post):	51	45	68	92	64

1. Write the Hypotheses:

H0:_______________, the mean difference in ___________ between ____________ and ______________ is _______________

Ha:_______________, the mean difference in ___________ between ____________ and ______________ is _______________

2. Are the conditions for inference met? (draw a picture of the histograms)

3. Provide the calculations:
   1. Sample diff:_________________________________
   2. Standard err:_____________________________________
   3. T-stat:__________________________________________
   4. P-value:_________________________________________
4. Write your conclusion:

At the 5% level of significance, we ______________ that the mean difference in ___________ between ____________ and ______________ is _______________. We ________________________ the mean difference in ___________ between ____________ and ______________ is _______________. [P-value = ________ ]

5. Construct a 90% Confidence interval.

6. What does the interval mean in the context of the problem.

We are 90% confident that the difference in mean _______________

For ________________________ is between ____________ and _______________ ___________________ than __________________.

7. Did the training improve Kara's striking skills? Explain

Answer 1

Let us denote by , the difference between  the post -pre values of the strike. The will be the average of the differences between post and pre values. If Kara has to show improvement then her strikes after the training has to be more than the pre training values. Let be the population mean of the difference.

1. Write the Hypotheses:

the mean difference in Strikes between post and pre is zero.

, the mean difference in strikes between post and pre is more than zero.

2. Are the conditions for inference met? (draw a picture of the histograms)

Yes the approximate conditions are met.

3.Provide the calculations:

Pre	post	diff	diff^2
29	51	22	484
32	45	13	169
44	68	24	576
34	92	58	3364
19	64	45	2025
	Total	162	6618

The mean difference:

Sample variance of the difference :

  

Standard deviation   

standard error =

The 90% confidence interval:

  

i). Sample difference: 32.4

ii). Standard Error = 8.2741

iii) T-stat : 3.9158

iv). p-value : 0.0087

v). Write your conclusions:

At the 5% level of significance, we observe that the mean difference in strikes between post training and Pre training is 32.4. We conclude that the mean difference in strikes between post and pre is significant. [P-value = 0.0087]

3. Construct 90% confidence interval:

i). What does the interval mean in the context of the problem.

We are 90% confident that the difference in mean strike

For strike is between 14.76 and 50.04 than containing zero

4.Did the training improve Kara's striking skills? Explain

Since the p-value for the test is 0.0087<0.5, we reject the null hypothesis and conclude that the there are enough evidence in the claim that training improve Kara's striking skills. Moreover, the 90% confidence interval doesn't contain zero which is also indicative of the claim.