Question

On a television show, eight contestants try to lose the highest percentage of weight in order to win a cash prize. As part of the show, the contestants are timed as they run an obstacle course. The table shows the times (in seconds) of the contestants at the beginning of the season and at the end of the season. At

α=0.05 is there enough evidence to support the claim that the contestants' times have changed? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below.

Contestant	Time_(beginning)	Time_(end)
1	116.4	116.1
2	111.1	111.4
3	103.1	102.9
4	130.2	129.8
5	135.2	135
6	116.5	116.4
7	136.1	136
8	101.3	100.9

1. Identify the claim and Ho and Ha

            What is the claim?

        

Let μd be the hypothesized mean of the difference in the times (beginning− end). What are Ho and Ha?

B. Find the critical value(s) and identify the rejection region(s).

C. Calculate dBAR and Sd.

(d) Find the standardized test statistic t.

E. (e) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

________the null hypothesis. There ____ enough evidence to _____the claim that the contestants times have _____.

Answer 1

Number	Time_(beginning)	Time_(end)	Difference
	116.4	116.1	0.3	0.015625
	111.1	111.4	-0.3	0.225625
	103.1	102.9	0.2	0.000625
	130.2	129.8	0.4	0.050625
	135.2	135	0.2	0.000625
	116.5	116.4	0.1	0.005625
	136.1	136	0.1	0.005625
	101.3	100.9	0.4	0.050625
Total	949.9	948.5	1.4	0.355

To Test :-

H0 :-

H1 :-

Test Statistic :-

t = 2.198

Test Criteria :-
Reject null hypothesis if

Critical value

Result :- Fail to reject null hypothesis

___Fail to ____the null hypothesis. There _insufficient / is not___ enough evidence to ___support __the claim that the contestants times have _changed____.