Bus Stats Exam #2 Questions

1, the z value is -1.645 where 5% area to the left. 2. ==6-1.645*0.3 The correct answer is: 5.5065

"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.)

yes

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 or no

b. [.21, .25]

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. a. [.21, .23] b. [.21, .25] c. [.23 ,.23] d. [.23, .27] e. None of these options is correct

a. [.09, .37]

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. a. [.09, .37] b. [.17, .29] c. [.21, .25] d. Cannot compute, does not satisfy necessary conditions for the distribution of sample proportions to be approximately normal. Feedback

a. becomes narrower

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 a. becomes narrower b. becomes wider c. does not change d. becomes 0.1

a. all values in an interval or collection of intervals

A continuous random variable may assume: a. all values in an interval or collection of intervals b. only integer values in an interval or collection of intervals c. only fractional values in an interval or collection of intervals d. all the positive integer values in an interval

a. is a continuous probability distribution

A normal probability distribution a. is a continuous probability distribution b. is a discrete probability distribution c. can be either continuous or discrete d. always has a standard deviation of 1

a. 0.1359

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 b. 0.8185 c. 0.3413 d. 0.4772

b. .0495

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 a. 0 b. .0495 c. .4505 d. None of the alternative answers is correct.

d. 0.0228

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 a. 0.5228 b. 0.9772 c. 0.4772 d. 0.0228

d. 0.5 and 0.050

A population of size 1,000 has a proportion of 0.5. Therefore, the expected value and the standard deviation of the sample proportion for samples of size 100 are a. 500 and 0.047 b. 500 and 0.050 c. 0.5 and 0.047 d. 0.5 and 0.050

a. 0.419 to 0.481

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 a. 0.419 to 0.481 b. 0.40 to 0.50 c. 0.45 to 0.55 d. 1.645 to 1.96

d. 0.0400

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 a. 0.0016 b. 0.2400 c. 0.1600 d. 0.0400

b. 24.4 to 25.6

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 Select one: a. 20.5 to 26.5 b. 24.4 to 25.6 c. 23.0 to 27.0 d. 20.0 to 30.0

a. 0.9772

A random variable X follows a normal distribution with mean = 2000 and standard deviation = 100. For a randomly selected sample of 16 observations, what is the probability that the sample mean is less than 2050? a. 0.9772 b. 0.0228 c. 0.0000 d. 0.3085

d. 170.2 to 189.8

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 a. 105.0 to 225.0 b. 175.0 to 185.0 c. 100.0 to 200.0 d. 170.2 to 189.8

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

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of is a. not normal since n < 30 b. approximately normal because is always normally distributed c. approximately normal if np ≥ 5 and n(1-p) ≥ 5 d. approximately normal if np > 30 and n(1-p) > 30

c. 0.0668

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 a. 0.4332 b. 0.9332 c. 0.0668 d. 0.5668

c. 0.0819

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 a. 0.8633 b. 0.6900 c. 0.0819 d. 0.0345

d. 1.993

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 a. 1.96 b. 1.64 c. 1.28 d. 1.993

c. 39.14 to 42.36

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 a. 40.75 to 42.36 b. 39.14 to 40.75 c. 39.14 to 42.36 d. 30 to 50

d. 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. The value of the margin of error at 95% confidence is a. 80.83 b. 7 c. 0.8083 d. 1.611

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

A standard normal distribution is a normal distribution with a. a mean of 1 and a standard deviation of 0 b. a mean of 0 and a standard deviation of 1 c. any mean and a standard deviation of 1 d. any mean and any standard deviation

b. becomes smaller

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution Select one: a. becomes larger b. becomes smaller c. stays the same d. becomes negative

c. standard error of the mean decreases

As the sample size increases, the a. standard deviation of the population decreases b. population mean increases c. standard error of the mean decreases d. standard error of the mean increases

e. 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(63 < x< 74)? a. None of these is correct b. 0.9931 c. 0.8729 d. 0.9772 e. 0.8501

a. 0.8729

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? a. 0.8729 b. 0.5000 c. 0.3729 d. 1.0000 e. None of them is correct

b. 0

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? a. 0.1271 b. 0 c. 0.8729 d. 0.3729 e. None of these is correct.

a. 0.9772

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? a. 0.9772 b. None of these is correct. c. 0.0228 d. 1 e. 0.5

a. 0.1271

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? a. 0.1271 b. 0.8729 c. 0 d. 0.3729 e. None of these is correct.

c. cumulative probabilities for a normally distributed x value

Excel's NORM.DIST function can be used to compute a. cumulative probabilities for a standard normal z value b. the standard normal z value given a cumulative probability c. cumulative probabilities for a normally distributed x value d. the normally distributed x value given a cumulative probability

d. the normally distributed x value given a cumulative probability

Excel's NORM.INV function can be used to compute a. cumulative probabilities for a standard normal z value b. the standard normal z value given a cumulative probability c. cumulative probabilities for a normally distributed x value d. the normally distributed x value given a cumulative probability

c. Approximately 50%.

For the past 10 years, the average high temperature on September 1 is 80° with a standard deviation of 5°. If the temperature is normally distributed, what is the probability that the high temperature on September 1 of next year will be between 80° and 95°? a. Approximately 25%. b. Approximately 33%. c. Approximately 50%. d. Approximately 100%

c. 0.75

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 a. 300 b. approximately 300 c. 0.75 d. 0.25

b. 1.22

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. a. 0.3888 b. 1.22 c. 2.22 d. 3.22

a. 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 0.1401? Use the Standard Normal Cumulative Probability Table. a. 1.08 b. 0.1401 c. 2.16 d. -1.08

c. 0.9

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be a. 0.1 b. 0.95 c. 0.9 d. 0.05

a. the size of the confidence interval to increase

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect a. the size of the confidence interval to increase b. the size of the confidence interval to decrease c. the size of the confidence interval to remain the same d. the sample size to increase

b. Better chance he is not good at selling the product

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? a. Better chance he had a bad week b. Better chance he is not good at selling the product

e. 0.0062

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) a. 0.0228 b. 0.2554 c. 0.1234 d. None of these answers is correct e. 0.0062

b. 0.0228

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 that the sample mean is long enough? (Type B) a. None of these answers is correct b. 0.0228 c. 0.9772 d. 0.3085 e. 0.0000

1984

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)

a. 0.52 to 0.68

In a random sample of 144 observations, = 0.6. The 95% confidence interval for P is a. 0.52 to 0.68 b. 0.144 to 0.200 c. 0.60 to 0.70 d. 0.50 to 0.70

d. 0.071 to 0.129

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is a. 0.871 to 0.929 b. 0.120 to 0.280 c. 0.765 to 0.835 d. 0.071 to 0.129

b. the sample standard deviation is used to estimate the population standard deviation

In interval estimation, the t distribution is applicable only when a. the population has a mean of less than 30 b. the sample standard deviation is used to estimate the population standard deviation c. the variance of the population is known d. the standard deviation of the population is known

c. 60 sample-1 (61-1=60)

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 a. 22 b. 23 c. 60 d. 61

d. 8.61 to 9.39 hours

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 a. 7.04 to 110.96 hours b. 7.36 to 10.64 hours c. 7.80 to 10.20 hours d. 8.61 to 9.39 hours

d. 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. The standard error of the mean is a. 7.50 b. 0.39 c. 2.00 d. 0.20

a. 0.39

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 a. 0.39 b. 1.96 c. 0.20 d. 1.64

b. 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 lower bound of the 95% confidence interval? a. 13.97 b. 14.22 c. 14.36 d. 15.00 e. 14.23

c. 15.78

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? a. 15.00 b. 15.29 c. 15.78 d. 15.77 e. 16.5

1. z value is 1.96 where 2.5% area to the right. 2. =20+1.96*8 The correct answer is: 35.68

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.)

1, the z value is 1.285 where 10% area to the right. 2. =20+1.285*8 The correct answer is: 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 .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.)

c. 36 and 1.86

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) a. 8.7 and 1.94 b. 36 and 1.94 c. 36 and 1.86 d. 36 and 8

d. None of these options is correct

Suppose we try to estimate the average money spend by customers. Two different random samples of 100 data values are taken from the large population. One sample has a larger sample standard deviation than the other. Each of the samples is used to construct a 95% confidence interval. How do you think these two confidence intervals would compare? a. The two samples would produce identical values for the lower and upper bounds of the two confidence intervals. b. The two confidence intervals would have the same width because they are both 95% intervals. c. The confidence interval based on the sample with the small standard deviation would be wider. d. None of these options is correct

a. central limit theorem

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 a. central limit theorem b. fact that there are tables of areas for the normal distribution c. assumption that the population has a normal distribution d. All of these answers are correct.

d. could be any value

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 a. is 14 b. is 15 c. is 15.1581 d. could be any value

b. is 14

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 mean a. is 5 b. is 14 c. is 4 d. cannot be determined because the population is infinite

b. 1.581

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) a. 2.500 b. 1.581 c. 2.000 d. 1.414

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

The sampling distribution of the sample mean a. is the probability distribution showing all possible values of the sample mean b. is used as a point estimator of the population mean μ c. is an unbiased estimator d. shows the distribution of all possible values of μ

b. standard error of the mean

The standard deviation of all possible values is called the a. standard error of proportion b. standard error of the mean c. mean deviation d. central variation

d. standard error of the proportion

The standard deviation of is referred to as the a. standard proportion b. sample proportion c. average proportion d. standard error of the proportion

d. None of the alternative answers is 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. a. 0.5 b. 1.0 c. 0.3413 d. None of the alternative answers is correct.

d. 0.0440

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. a. 0.4772 b. 0.4332 c. 0.9104 d. 0.0440

c. 0.1587

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? a. 0.3413 b. 0.8413 c. 0.1587 d. 0.5000

a. the weight of items produced by a machine

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 b. 8 ounces c. 2 ounces d. the normal distribution

c. 3.22%

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. a. 46.78% b. 96.78% c. 3.22% d. 53.22%

d. 0.4617

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? a. 0.1145 b. 0.2881 c. 0.1736 d. 0.4617

b. becomes wider

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, α, is decreased, the interval for the population proportion (Hint: check textbook section 8.1 for the definition of level of significance) a. becomes narrower b. becomes wider c. does not change d. remains the same

a. 0.000

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.) a. 0.000 b. 0.0055 c. 0.4945 d. 0.9945

c. 0.0069

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.) a. 0.000 b. 0.4931 c. 0.0069 d. 0.9931

a. 0.0029

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 b. 0.0838 c. 0.4971 d. 0.9971

d. 0.9190

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.) a. 0.0222 b. 0.4190 c. 0.5222 d. 0.9190

a. 0.9525 b. 0.8607 c. 0.8599

Z is a standard normal random variable. Compute the following probabilities. Please keep four decimal places. a. P(z ≤ 1.67) b. P(-1.33 ≤ z ≤ 1.67) c. P(z > -1.08)

d. Unbiased

__________ 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. a. ​Predictable b. ​Precise c. ​Symmetric d. Unbiased

b. 1979

magine 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 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) a. 1929 b. 1979 c. None of these answers is correct. d. 1836 e. 2021