Managerial Statistics

1) In a sample of 162 companies, 104 reported profits that beat the prior estimates, 29 reported profits that matched the prior estimates, 29 reported profits that fell short of the prior estimates.

a) Produce a point estimate for the proportion of companies that fell short of the prior estimates.

b) Calculate the margin of error for a confidence interval of 95% for the ones who matched the prior estimates.

c) Construct a 90% confidence interval for the ones who matched the prior estimates.

d) What should be the size of the sample for the margin of error to be 0.01, for a confidence level of 88% and for the ones who beat the prior estimates.

2) A population is subjected to a statistical research in order to observe the prevalence of a particular feature. A random sample of 135 (n) elements are chosen from the population. The proportion of the addressed feature is observed on 25% (p̂ ) of them.

a) What is the standard error of the sample proportion? b) What is the probability that the sample proportion is more than 0.17? c) What is the probability that the sample proportion is between 0.18 and 0.23?

3) Scores of a test are normally distributed with a mean of 280 and a standard deviation of 60. A random sample of 9 test scores was taken.

a) What is the standard error of the sample mean score? b) What is the probability that the sample mean score is less than 270? c) What is the probability that the sample mean score is more than 250?