5. PART A: Data was randomly collected from 80 CEOSand the 99% confidence interv

Question

5. PART A:

Data was randomly collected from 80 CEOSand the 99% confidence interval for the mean was calculated to be ($2,181,260 , $5,836,180.) What additional assumption is necessary for the confidence interval to be valid?

a. None. The central limit theorem applies.

b. The population of the total compensation of CEO's in the service industry is approximately normally distributed.

c. The distribution of the sample mean is approximately normal.

d. The sample standard deviation is less than the degree of freedom.

PART B:

45 CEO's average salaries are in the interval of (123,041 , 140,104). It is desired to reduce the width of the confidence interval. Which of the following result in a reduced interval width AND WHY?

a. Increase sample size and confidence level

b. Increase sample size and decrease confidence level.

c. Decrease sample size and decrease confidence level

d. Decrease sample size and increase confidenence level.

PART C:

Which statement describes a parameter?

a. an unbiased estimate of a statistic found by experimentation or polling

b. a parameter is a numerical measure of a population that is almost always unknown and must be estimated.

c. A parameter is level of confidence associated with an interval about a sample mean or population

Explanation / Answer

Part A: Correct Answer: Option (C) The distribution of the sample mean is approximately normal.

Since the central limit theorem in it's shortest form states that the sampling distribution of the sampling means approaches a normal distribution as the sample size gets larger, regardless of the shape of the population distribution. So the sample means will be normally distributed (especially when the sample is above 30) if the population is positively skewed, negatively skewed or even binomial (having only 2 outcomes).

Part B: Correct Answer: option (b) . Increase sample size and decrease confidence level.

since i) Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error.

ii) Decreasing the confidence level decreases the width of confidence intervals, because it decreases the critical values

Part C: Correct answer: Option (B) a parameter is a numerical measure of a population that is almost always unknown and must be estimated.

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