SOLUTION: 5. A researcher claims that the average age of people who buy lottery tickets is 65. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation i

Algebra ->  Probability-and-statistics -> SOLUTION: 5. A researcher claims that the average age of people who buy lottery tickets is 65. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation i      Log On


   

Question 310647: 5. A researcher claims that the average age of people who buy lottery tickets is 65. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 14. At α = 0.05 is there enough evidence to reject the researcher’s claim? Show all work.
49
63
80
52
22
80
72
56
70
56

24
46
70
74
70
61
65
71
39
74

79
76
71
49
62
68
71
67
69
45
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!



_
x = 61.7, sigma = 14

H%5B0%5D: mu=65
H%5Ba%5D: mu%3C%3E65


z=%28xBAR-mu%29%2F%28sigma%2Fsqrt%28n%29%29=%2861.7-65%29%2F%2814%2Fsqrt%2830%29%29=-1.29

No, we cannot reject the claim at alpha=0.05 because z 
is neither less than -1.96 nor greater than 1.96.

We could also do it by computing the p-score, the probability
that xBAR would be at least as far off from 65 as 61.7 if the mean 
were actually 65.     

To find that p-score we find the area to the left of the z-score -1.29
as .5-.4015=.0985 and double it since this is a two-tail test.  That
gives the p-score of .197.

So we would only reject the null hypothesis if it were that alpha%3E.197.
But alpha is lower that that, only .05.

Edwin