Intelligence quotients (i.e. IQ's) as measured by one intelligence test are
known to be normally distributed with a standard deviation of 16. Suppose a random sample of X denote the mean IQ score achieved on the test by 20 people take this intelligence test. Let this sample of 20 people.
Suppose that, instead of using a sample of size 20, it was decided that the size of the sample should be such that, in using the sample mean X to estimate the population mean , the 95% maximum error of the estimate should be 2.5. What should the sample size be to achieve this?
(A) 12 (B) 13 (C) 39 (D) 40 (E) 62 (F) 63 (G) 120 (H) 121 (I) 157 (J) 158
Does the gender of employees have a bearing upon how they feel about their
supervisors? In one large company, independent random samples of male and female employees were obtained and the results summarized in the following table.
See attached file for full problem description.
(32) In estimating the proportion of female employees of this company who have favorable opinions of their supervisors, the 99% margin of error (or error bound) is:
(A) .0496 (B) 0.1155 (C) 0.1738 (D) 0.0639 (E) 0.2036 (F) 0.1918 (G) 0.2557 (H) 0.1508 (I) 0.2227 (J) 0.1279
(33) Is there any difference in opinions about supervisors between the male and female
employees of this company? In testing the appropriate set of hypotheses with the given data, the numerical value of the test statistic is calculated as TS=1.36. What is the P-value for this result?
(A ) 0.9031 (B) 0.0869 (C) 0.1738 (D) 0.4515 (E) 0.3476 (F) 0.2607 (G) 0.5485 (H) 0.6524 (I) 0.7393 (J) 0.8262
(34) In estimating the difference between the proportions of male and female employees having favourable opinions of their supervisors, the standard error of the estimate is estimated by:
(A) 0.1023 (B) 0.0044 (C) 0.2570 (D) 0.0660 (E) 0.0424 (F) 0.2121 (G) .0889 (H) 0.1482 (I) 0.3035 (J) 0.1667
The solution gives the answers to multiple choice questions from testing of hypothesis and sample size determination.