. A researcher claims that the average age ofpeople who buy theatre tickets is 5
ID: 2955011 • Letter: #
Question
. A researcher claims that the average age ofpeople who buy theatre tickets is 50. A sample of 30 is selectedand their ages are recorded as shown below. The standard deviationis 5. At = 0.05 is there enough evidence to reject theresearcher’s claim? Show all work.
50
46
54
48
52
49
46
44
48
53
44
49
57
60
58
51
56
50
55
53
45
52
45
60
52
59
54
59
51
59
1. Given a level ofconfidence of 99% and a population standard deviation of 10, whatother information is necessary:
(A) To find the Maximum Error of Estimate (E)?
(B) To find the sample size (n)?
(C) Given the above confidence level and population standarddeviation, find the Maximum Error of Estimate (E) if n = 30. Show all your calculations. Show all work.
(D) For this same sample of n = 30, what is the width of theconfidence interval around the population mean? Show allwork.
(E) Given this same confidence level and standard deviation, find nif E = 5.0. (Always round to the nearest whole person.) Showall work.
50
46
54
48
52
49
46
44
48
53
44
49
57
60
58
51
56
50
55
53
45
52
45
60
52
59
54
59
51
59
Explanation / Answer
Given n=30, xbar=51.97 (based on the data), s=5 =0.05, |Z(0.025)|=1.96 (check normal table) The test hypothesis is Ho:=50 Ha: not equal 50 The test statistic is Z=(xbar-)/(s/n) =(51.97-50)/(5/sqrt(30)) = 2.16 Since Z=2.16>1.96, we reject Ho. So there is enough evidence toreject the researcher’s claim.
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