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# Goodness of Fit Test: Telephone Calls Received

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8. During 200 randomly selected minutes, the number of telephone calls received each minute were recorded. At the .05 level of significance, is there any evidence that these data are not Poisson with a mean of 2.8?

Number of
Calls Per Observed
Minute Frequency
0 11
1 46
2 50
3 47
4 28
5 11
6 or more 7

(a) What are the null and alternate hypotheses?
(b) Let X = number of calls per minute. What is the expected frequency of the class X = 3?

9. The following distribution shows the frequencies of aptitude test scores for a random sample of 60 test takers. At the .10 level of significance, is there any evidence that these data are NOT normally distributed with a mean of 72 and a standard deviation of 8?
Observed
CLASS Frequency
50 ? X < 60 10
60 ? X < 70 18
70 ? X < 80 24
80 ? X < 90 6
90 ? X < 100 2

(a) What are the null and alternate hypotheses?
(b) Let X = an aptitude test score. Find the expected frequency of the class: 80 ? X < 90.