12 MCQs

1. The histogram below shows the income distribution pattern of households in the small town of Finedale. Each month, to approximate the average income in the town, the local newspaper surveys 50 randomly-selected households and averages their reported incomes. The survey has been repeated once a month for 3 years.
If the distribution of the average incomes from the 36 samples is graphed, the distribution will be:
Skewed strongly to the left.
Skewed strongly to the right.
Approximately Normal.
Bimodal.

2. A nutrition researcher wants to determine the mean fat content of hen’s eggs. She collects a sample of 40 eggs. She calculates a mean fat content of 23 grams, with a sample standard deviation of 8 grams.
What is the 95% confidence interval for this sample?
[22.6 grams; 23.4 grams].
[7.0 grams; 39.0 grams].
[20.5 grams; 25.5 grams].
[19.7 grams; 26.3 grams].

3. A market researcher plans to sample sales receipts at a natural food store to estimate the average size (in dollars) of a customer purchase. Previous analysis suggests that the standard deviation of the purchase amount is approximately $25.
In order to calculate a 95% confidence interval of total width less than $5, how many sales records should the researcher include in her sample?
97.
271.
385.
The answer can not be determined from the information provided.

4. When calculating a confidence interval for a mean, which of the following measures will reduce the width of the confidence interval?
Increasing the confidence level.
Decreasing the sample size.
Increasing the sample size.
None of the above.

5. In a sample of 6 software developers, the mean length of the work week is 60 hours, with standard deviation 5 hours.
What is the 95% confidence interval for the average work week in the software development trade?
[54.8, 65.2].
[55.4, 64.6].
[56.6, 63.4].
[56.0, 64.0].

6. The Kingston Review (KR) is testing a new GMAT question. The KR wants to determine what proportion of test-takers will answer the question correctly, in order to assess its difficulty. In a random sample of 144 test-takers, 75% answered the question correctly.
What is the 95% confidence interval for the proportion of test-takers answering the question correctly?
[65.7%, 84.3%]
[67.9 %, 82.1 %]
[69.1%, 80.9%]
The answer can not be determined from the information provided.

7. A filling machine in a brewery is designed to fill bottles with 355 ml of hard cider. In practice, however, volumes vary slightly from bottle to bottle. The brewer suspects that the filling machine has been underfilling the bottles. In a sample of 49 bottles, the mean volume of cider is found to be 354 ml, with a standard deviation of 3.5 ml. To determine if the machine is underfilling bottles, the brewer performs a one-sided hypothesis test.
The best formulation of the null hypothesis is:
The true mean cider volume of each bottle is 354 ml.
The true mean cider volume of each bottle is at least 355 ml.
The machine is underfilling the bottles.
The machine is underfilling the bottles by 1 ml.

8. After a series of major corporations admitted to large accounting irregularities, a public policy research institute conducts a survey to determine whether the public favors increased governmental regulation and oversight of corporations.
Which of the following questions will deliver an unbiased response?
In light of the recent wave of shocking corporate accounting fraud, should government increase its regulation and oversight of corporations?
Should privately-owned companies be subjected to intrusive governmental regulation and oversight?
Is the government doing enough to protect American shareholders from corporate greed? None of the above.

9. In a move to improve relations with employees, the human resource manager of a company with multiple departments (marketing, information technology, accounting, etc.) wants to send surveys out to 50 employees. The surveys contain questions about employees’ job satisfaction.
In order to get the most representative responses, to whom should the manager send the surveys?
To 50 employees in a randomly selected department.
To 50 employees selected by an election to represent the workforce.
To 50 employees selected randomly by drawing their names from a pool of all employees.
To the 50 most recent hires.

10. GMAT scores are reported to be distributed normally, with a mean of around 520.
Approximately ninety-five percent of all test-takers’ scores will fall:
Within 1 standard deviation of the mean.
Within 2 standard deviations of the mean.
Within 3 standard deviations of the mean.
Above the mean.

11. In a finance class, the midterm exam’s scores were distributed approximately normally, with mean 13 (out of 20), and standard deviation 4.
Approximately what proportion of the test takers scored no higher than 17?
16%.
32%.
68%.
84%.

12. Which of the following is not true about the Normal Distribution?
It is completely described by its mean and its standard deviation.
Its median is equal to its mode.
Its median is equal to its mean.
The range of possible outcomes is finite.