Question

The owner of a health club franchise believes that the average age of the​ club's members is under

40

years. To test​ this, a random sample of

30

members was selected. The accompanying sample data are the ages of the sampled individuals.

24 45 65 21 40 19 34 57 40 50 21 20 46 47 36 26 63 67 18 21 60 28 36 45 23 52 61 21 35 36

Click the icon to view the data table.

a. State the appropriate null and alternative hypotheses.

b. Use the test statistic approach to test the null hypothesis with

alphaαequals=0.05

Answer 1

	Values ( X )
	24	212.1887
	45	41.3873
	65	698.7193
	21	308.5889
	40	2.0543
	19	382.8557
	34	20.8547
	57	339.7865
	40	2.0543
	50	130.7203
	21	308.5889
	20	344.7223
	46	55.2539
	47	71.1205
	36	6.5879
	26	157.9219
	63	596.9861
	67	808.4525
	18	422.9891
	21	308.5889
	60	459.3863
	28	111.6551
	36	6.5879
	45	41.3873
	23	242.3221
	52	180.4535
	61	503.2529
	21	308.5889
	35	12.7213
	36	6.5879
Total	1157	7093.3652

Mean

Standard deviation

To Test :-

H0 :-

H1 :-  

Test Statistic :-


t = -0.502

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 0.502 ) = 0.3097
Reject null hypothesis if P value < level of significance
P - value = 0.3097 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that the average age of the​ club's members is under 40 years.