Question

# The vice president of the student organization has asked you to create an estimate of the...

The vice president of the student organization has asked you to create an estimate of the proportion of students who have attained more than 60 credit hours. You ask her what level of confidence she wants to have in the estimate and she says that she would like to be 90% confident in the proportion estimate. Create the confidence interval using the sample data. Write a sentence or two to communicate the results to her.

 Student More than 60 credit hours attained 1 No 2 No 3 No 4 No 5 No 6 No 7 No 8 No 9 No 10 No 11 No 12 No 13 No 14 No 15 No 16 No 17 No 18 No 19 No 20 No 21 No 22 No 23 No 24 No 25 No 26 No 27 No 28 No 29 No 30 No 31 No 32 No 33 No 34 No 35 No 36 No 37 No 38 No 39 No 40 No 41 No 42 No 43 No 44 No 45 No 46 No 47 No 48 No 49 No 50 No 51 No 52 No 53 No 54 Yes 55 Yes 56 Yes 57 Yes 58 Yes 59 Yes 60 Yes 61 Yes 62 Yes 63 Yes 64 Yes 65 Yes 66 Yes 67 Yes 68 Yes 69 Yes 70 Yes 71 Yes 72 Yes 73 Yes 74 Yes 75 Yes 76 Yes 77 Yes 78 Yes 79 Yes 80 Yes 81 Yes 82 Yes 83 Yes 84 Yes 85 Yes 86 Yes 87 Yes 88 Yes 89 Yes

Number of students who have attained more than 60 credit hours = 36

proportion = p = 36/89 = 0.4045

confidence interval is given by:

p = proportion = 0.4045

z = z value for desired confindence level of 90% = 1.645

n= numbe of students = 89

Thus putting the values in above equation gives

confidence interval = (0.3189 , 0.4901)

Result : Thus we have 90% confidence that proportion of students who have attained more than 60 credit hours is between 31.89% and 49.01%.

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Thanks.

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