- 1 of 3 ID: MST.FET.E.CIMSU.01.0030A [4 marks] The national Menso organisation

Question

- 1 of 3 ID: MST.FET.E.CIMSU.01.0030A [4 marks] The national Menso organisation would like to estimate the average I.Q. of its members. A sample of 55 members complete an I.Q. test, and achieve an average score of 141. The standard deviation in this sample is 5.11 The population standard deviation is unknown. a) Select all the techniques that are commonly used to construct a confidence interval for the menso mean when the population standard deviation (o) is unknown Approximate the population standard deviation (o) with the sample standard deviation Replace the sample size (n) with n-1 Decrease the confidence level to compensate for the increased margin of error OApproximate the standard normal distribution with the Student's t distribution b) Calculate the upper and lower bounds of the 90% confidence interval for the average l Q in Mensa. You may find this Student's t distribution table useful. Give your answers to 2 decimal places. Upper bound Lower bound

Explanation / Answer

Answer :

A) approximate the population standard decoration with sample standard deviation.

Approximate the standard normal distribution with t distribution.

B) Confidence interval = mean (+/-) t*s/sqrt(n)

Degree of freedom n-1 = 54

CI = 141 (+/-) 1.673565*5.11/?55 = 141 (+/-) 1.15314

Lower bound = 139.8468

Upper bound = 142.15314

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