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Chapter 5: Q24E (page 314)

Salary of a travel management professional. According to the most recent Global Business Travel Association (GBTA) survey, the average base salary of a U.S. travel management professional is \(94,000. Assume that the standard deviation of such salaries is \)30,000. Consider a random sample of 50 travel management professionals and let 蠂炉 represent the mean salary for the sample.

  1. What is渭蠂炉?
  2. What is蟽蠂炉?
  3. Describe the shape of the sampling distribution of蠂炉.
  4. Find the z-score for the value蠂炉=86,660
  5. FindP蠂炉>86,660.

Short Answer

Expert verified

Anyone who makes a career doing anything that needs a specific degree of knowledge, ability, as well as experience is referred to as a professional.

Step by step solution

01

(a) The data is given below

The calculation is given below:

Given,

渭=94,000蟽=30,000n=50

渭蠂炉=渭0=94000渭蠂炉=94000

02

(b) The data is given below

The calculation is given below:

蟽蠂炉=蟽n=30,00050=4242.64068712鈮�4242.6407

蟽蠂炉=4242.6407

03

(c) The data is given below

The calculation is given below:

As here n鈮�30

As a result, the sample size is sufficient to follow the normal distributions. As a result, the distribution's form is normal.

The chart is given below:

04

(d) The data is given below

The calculation is given below:

Zscore=蠂-渭蟽/n


蠂=86660渭=94000n=50

Zscore=86660-940004242.6407=-1.73

05

(e) The data is given below

The calculation is given below:

P蠂炉>8660=1-P蠂炉<8660=1-P蠂炉-渭蠂炉蟽蠂炉<8660-940004242.6407=1-PZ<-1.73

Standard normal table:

=1-0.9581848=0.0418152鈮�0.0418P蠂炉>86660=0.0418

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Most popular questions from this chapter

Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of the power quality (sags and swells) of a transformer, Exercise 2.76 (p. 110). For transformers built for heavy industry, the distribution of the number of sags per week has a mean of 353 with a standard deviation of 30. Of interest is , that the sample means the number of sags per week for a random sample of 45 transformers.

a. FindE蠂炉 and interpret its value.

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  1. Describe the sampling distribution of X炉.
  2. If the mean for the 6,000 undergraduate students is渭= 18.5 years, findPx炉>19.1.
  3. If the mean for the 6,000 undergraduate students is渭= 19.5 years, findPx炉>19.1.
  4. If,P(x炉>19.1)=0.5 what is渭?
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Switching banks after a merger. Banks that merge with others to form 鈥渕ega-banks鈥� sometimes leave customers dissatisfied with the impersonal service. A poll by the Gallup Organization found 20% of retail customers switched banks after their banks merged with another. One year after the acquisition of First Fidelity by First Union, a random sample of 250 retail customers who had banked with First Fidelity were questioned. Letp^ be the proportion of those customers who switched their business from First Union to a different bank.

  1. Find the mean and the standard deviation of role="math" localid="1658320788143" p^.
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Refer to Exercise 5.3. Assume that a random sample of n = 2 measurements is randomly selected from the population.

a. List the different values that the sample median m may assume and find the probability of each. Then give the sampling distribution of the sample median.

b. Construct a probability histogram for the sampling distribution of the sample median and compare it with the probability histogram for the sample mean (Exercise 5.3, part b).

Question: The standard deviation (or, as it is usually called, the standard error) of the sampling distribution for the sample mean, x炉 , is equal to the standard deviation of the population from which the sample was selected, divided by the square root of the sample size. That is

蟽X炉=蟽n

  1. As the sample size is increased, what happens to the standard error of? Why is this property considered important?
  2. Suppose a sample statistic has a standard error that is not a function of the sample size. In other words, the standard error remains constant as n changes. What would this imply about the statistic as an estimator of a population parameter?
  3. Suppose another unbiased estimator (call it A) of the population mean is a sample statistic with a standard error equal to

蟽A=蟽n3

Which of the sample statistics,x炉or A, is preferable as an estimator of the population mean? Why?

  1. Suppose that the population standard deviation 蟽is equal to 10 and that the sample size is 64. Calculate the standard errors of x炉and A. Assuming that the sampling distribution of A is approximately normal, interpret the standard errors. Why is the assumption of (approximate) normality unnecessary for the sampling distribution ofx炉?
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