Econ 2030 Exam #2

Assume that our sample data of height in inches data represents the population of students at UMD and that this population is approximately normal with mean = 70 inches and standard deviation = 3.5 inches. Let x = height in inches (a continuous, normally distributed random variable) What is P(x = 74), ie. probability that x equals to 74?

0

X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is (Use the Standard Normal Cumulative Probability Table.)

0.000

Imagine a business is worried about one of its salespeople's performance. The population proportion of contacts leading to sales = 0.20. Imagine Charlie has contacted 100 customers this week but only made 10 sales (assume these contacts are a simple random sample of those who could have been called upon). What is the probability that a random sample of 100 customers made less than or equal to 10 sales, i.e. the sample proportion ≤ 10/100)? (Type A)

0.0062

Imagine we are trying to sell to a customer who demands that the mean of a random sample of 16 bulbs lasts at least 2,050 hours before they will buy. The population mean = 2,000 hours, and the population standard deviation is 100 hours. Assume that it is known bulb life is normally distributed. What is the probability we get the sale, i.e. the probability the sample mean is long enough? (Type B)

0.0228

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

0.071 to 0.129

Assume that our sample data of height in inches data represents the population of students at UMD and that this population is approximately normal with mean = 70 inches and standard deviation = 3.5 inches. Let x = height in inches (a continuous, normally distributed random variable) What is P(x > 74), ie. probability that x is bigger or equal to 74?

0.1271

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. Refer to Exhibit 8-1. The standard error of the mean is

0.20

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. Refer to Exhibit 8-1. With a 0.95 probability, the margin of error is approximately

0.39

A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate A is

0.419 to 0.481

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What percentage of items will weigh between 6.4 and 8.9 ounces?

0.4617

In a random sample of 144 observations, p-bar= 0.6. The 95% confidence interval for P is

0.52 to 0.68

Four hundred registered voters were randomly selected asked whether gun laws should be changed. Three hundred said "yes," and one hundred said "no." Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond "yes" is (Hint: page 16 of ppt file)

0.75

Assume that our sample data of height in inches data represents the population of students at UMD and that this population is approximately normal with mean = 70 inches and standard deviation = 3.5 inches. Let x = height in inches (a continuous, normally distributed random variable) What is P(63 < x< 74)?

0.8501

Assume that our sample data of height in inches data represents the population of students at UMD and that this population is approximately normal with mean = 70 inches and standard deviation = 3.5 inches. Let x = height in inches (a continuous, normally distributed random variable) What is P(x < 74), ie. probability that x less than 74?

0.8729

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be

0.9

Assume that our sample data of height in inches data represents the population of students at UMD and that this population is approximately normal with mean = 70 inches and standard deviation = 3.5 inches. Let x = height in inches (a continuous, normally distributed random variable) What is P(x > 63), ie. probability that x is bigger than 63?

0.9772

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.1401? Use the Standard Normal Cumulative Probability Table.

1.08

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.1112? Use the Standard Normal Cumulative Probability Table.

1.22

The following data was collected from a simple random sample from a process (an infinite population). 13 15 14 16 12 Refer to Exhibit 7-1. The point estimate of the population standard deviation is (Hint: page 16 of ppt file)

1.581

A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of $7.00. Refer to Exhibit 8-6. The value of the margin of error at 95% confidence is

1.611

A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of $7.00. Refer to Exhibit 8-6. If we want to determine a 95% confidence interval for the average hourly income, the value of "t" statistics is

1.993

Office workers receive an average of 15.0 faxes per day with a sample size of 80 and sample standard deviation of 3.5. Based on this information construct and interpret a 95% confidence interval for the mean. What is the lower bound of the 95% confidence interval

14.22

Office workers receive an average of 15.0 faxes per day with a sample size of 80 and sample standard deviation of 3.5. Based on this information construct and interpret a 95% confidence interval for the mean. What is the upper bound of the 95% confidence interval?

15.78

A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is

170.2 to 189.8

Imagine we are trying to sell to a customer who demands that the mean of a random sample of 16 bulbs lasts at least 2,050 hours before they will buy. The population mean = 2,000 hours, and the population standard deviation is 100 hours. Imagine that we are not sure of the distribution so the customer says we should increase the sample size to 64. What mean length of bulb life could you be 95% confident that the sample mean will be at least that long? (Type D)

1979

Imagine we are trying to sell to a customer who demands that the mean of a random sample of 64 bulbs lasts at least 2,050 hours before they will buy. The population mean = 2,000 hours, and the population standard deviation is 100 hours. What mean length of bulb life could you be 90% confident that the sample mean will be at least that long? (Use the Standard Normal Cumulative Probability Table. Round to nearest integer)

1984

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is

24.4 to 25.6

Pep Zone sells auto parts and supplies including a popular multi-grade motor oil. It has been determined that demand during replenishment lead-time is normally distributed with a mean of 20 gallons and a standard deviation of 8 gallons. If the manager of Pep Zone wants the probability of a stockout during replenishment lead-time to be no more than .10, what should the reorder point be? (Use the Standard Normal Cumulative Probability Table. If you can not find the exactly probability on the table, check page 32 of the ppt file. Just enter the number without any units. Keep two decimal places.)

30.28

Pep Zone sells auto parts and supplies including a popular multi-grade motor oil. It has been determined that demand during replenishment lead-time is normally distributed with a mean of 20 gallons and a standard deviation of 8 gallons. If the manager of Pep Zone wants the probability of a stockout during replenishment lead-time to be no more than .025, what should the reorder point be? (Use the Standard Normal Cumulative Probability Table, just enter the number without any units. Keep two decimal places.)

35.68

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Refer to Exhibit 7-5. The mean and the standard deviation of the sampling distribution of the sample means are (Hint: this is a finite population question, we need the finite population correction factor, see page 21 of the ppt file)

36 and 1.86

A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of $7.00. Refer to Exhibit 8-6. The 95% confidence interval for the average hourly wage of all information system managers is

39.14 to 42.36

"DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed. Ninety-five percent of the bottles will contain at least how many ounces? (Use the Standard Normal Cumulative Probability Table. Check page 32 on ppt file for an example. Just enter the number without any units. Keep four decimal places.)

5.5065

In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is

60

Assume that our sample data of height in inches data represents the population of students at UMD and that this population is approximately normal with mean = 70 inches and standard deviation = 3.5 inches. Let x = height in inches (a continuous, normally distributed random variable) What height is there a 2.5% chance that a randomly drawn student would be shorter than that height?

63.14

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is

8.61 to 9.39 hours

Imagine a business is worried about one of its salespeople's performance. The population proportion of contacts leading to sales = 0.20. Imagine Charlie has contacted 100 customers this week but only made 10 sales (assume these contacts are a simple random sample of those who could have been called upon). Charlie says he just had a bad week. You think Charlie is probably not very good at his job. Which of the following explanations is more likely to be true?

Better chance he is not good at selling the product

Given your answer to 1 and 2, is it likely another sample would have a mean of at least 16.5 faxes/day?

No, it would not be likely to have a sample mean of at least 16.5 faxes/day.

23% of executives believe an employer has no right to read employee's email. With a sample size of 25 construct a 90% confidence interval for the proportion.

[.09, .37]

23% of executives believe an employer has no right to read employee's email. With a sample size of 1200 construct a 90% confidence interval for the proportion.

[.21, .25]

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is (Use the Standard Normal Cumulative Probability Table.)

a. 0.0029 Correct

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the mean from that sample will be between 183 and 186 is

a. 0.1359 Correct

A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is 15. a. With 95% confidence, what is the margin of error? (Specify to 2 decimal places. Round the final answer, no rounding on intermediate steps) b. Compute the 95% confidence interval for the population mean (Specify to 2 decimal places).

a. 3.80 b. [76.20 , 83.80]

The sampling distribution of the sample mean

a. is the probability distribution showing all possible values of the sample mean Correct

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What is the random variable in this experiment?

a. the weight of items produced by a machine Correct

A continuous random variable may assume

all values in an interval or collection of intervals

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is

b. .0495 Correct

A standard normal distribution is a normal distribution with

b. a mean of 0 and a standard deviation of 1 Correct

The standard deviation of all possible values is called the

b. standard error of the mean Correct

A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval for μ

becomes narrower

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller

Using an α = 0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion

becomes wider

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is (Use the Standard Normal Cumulative Probability Table.)

c. 0.0069 Correct

A sample of 400 observations will be taken from a process (an infinite population). The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

c. 0.0668 Correct

A sample of 51 observations will be taken from a process (an infinite population). The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is

c. 0.0819 Correct

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What is the probability that a randomly selected item will weigh more than 10 ounces?

c. 0.1587 Correct

c. Assume that the same sample mean was obtained from a sample of 120 items. With 95% confidence, what is the margin of error? (Specify to 2 decimal places. Round the final answer, no rounding on intermediate steps) d. Compute the 95% confidence interval for the population mean (Specify to 2 decimal places). With 120 sample items.

c. 2.68 d. [77.32, 82.68]

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What percentage of items will weigh at least 11.7 ounces? Use the Standard Normal Cumulative Probability Table.

c. 3.22% Correct

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of is

c. approximately normal if np ≥ 5 and n(1-p) ≥ 5 Correct

As the sample size increases, the

c. standard error of the mean decreases Correct

The fact that the sampling distribution of the sample mean can be approximated by a normal probability distribution whenever the sample size is large is based on the

central limit theorem

The following data was collected from a simple random sample from a process (an infinite population). 13 15 14 16 12 Refer to Exhibit 7-1. The mean of the population (Hint: page 16 of ppt file)

could be any value

Excel's NORM.DIST function can be used to compute

cumulative probabilities for a normally distributed x value

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is

d. 0.0228 Correct

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were females. The standard error of the proportion of females is

d. 0.0400 Correct

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What is the probability that a randomly selected item will weigh between 11 and 12 ounces? Use the Standard Normal Cumulative Probability Table.

d. 0.0440 Correct

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

d. 0.5 and 0.050 Correct

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that x is between 1.48 and 15.56 is (Use the Standard Normal Cumulative Probability Table.)

d. 0.9190 Correct

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What is the probability that a randomly selected item weighs exactly 8 ounces? Use the Standard Normal Cumulative Probability Table.

d. None of the alternative answers is correct. Correct

__________ is a property of a point estimator that is present when the expected​ value of the point estimator is equal to the population parameter it estimates.

d. Unbiased Correct

The standard deviation of p-bar is referred to as the

d. standard error of the proportion Correct

Excel's NORM.INV function can be used to compute

d. the normally distributed x value given a cumulative probability Correct

he following data was collected from a simple random sample from a process (an infinite population). 13 15 14 16 12 Refer to Exhibit 7-1. The point estimate of the population mean (Hint: page 16 of ppt file)

is 14

A normal probability distribution

is a continuous probability distribution

σ xbar

is referred to as the standard error of the mean

In interval estimation, the t distribution is applicable only when

the sample standard deviation is used to estimate the population standard deviation Correct

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect

the size of the confidence interval to increase

23% of executives believe an employer has no right to read employee's email. With a sample size of 1200 construct a 90% confidence interval for the proportion. Does this sample satisfy the necessary conditions such that the distribution of sample proportions is approximately normal?

yes