stats 6, 7, 8

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?

1984

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

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?

35.68

"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

5.5065

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 Select one: a. 0.39 b. 1.96 c. 0.20 d. 1.64

a. 0.39

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

a. 0.52 to 0.68

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

a. the size of the confidence interval to increase

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.) Select one: a. 0.000 b. 0.0055 c. 0.4945 d. 0.9945

a. 0.000

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.) Select one: a. 0.0029 b. 0.0838 c. 0.4971 d. 0.9971

a. 0.0029

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 Select one: a. 0.1359 b. 0.8185 c. 0.3413 d. 0.4772

a. 0.1359

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 Select one: a. 0.419 to 0.481 b. 0.40 to 0.50 c. 0.45 to 0.55

a. 0.419 to 0.481

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. Select one: a. 1.08 b. 0.1401 c. 2.16 d. -1.08

a. 1.08

A continuous random variable may assume Select one: 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. all values in an interval or collection of intervals

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

a. becomes narrower

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 Select one: 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.

a. central limit theorem

A normal probability distribution Select one: 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. is a continuous probability distribution

The sampling distribution of the sample mean Select one: 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

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

Exhibit 6-5 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? Select one: a. the weight of items produced by a machine b. 8 ounces c. 2 ounces d. the normal distribution

a. the weight of items produced by a machine

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

b. 24.4 to 25.6

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

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

b. becomes wider

In interval estimation, the t distribution is applicable only when Select one: 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

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

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

b. .0495

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. Select one: a. 0.3888 b. 1.22 c. 2.22 d. 3.22

b. 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) Select one: a. 2.500 b. 1.581 c. 2.000 d. 1.414

b. 1.581

A standard normal distribution is a normal distribution with Select one: 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. a mean of 0 and a standard deviation of 1

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 (Hint: page 16 of ppt file) Select one: a. is 5 b. is 14 c. is 4 d. cannot be determined because the population is infinite

b. is 14

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

b. standard error of the mean

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

c. 0.9

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 Select one: a. 40.75 to 42.36 b. 39.14 to 40.75 c. 39.14 to 42.36 d. 30 to 50

c. 39.14 to 42.36

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 Select one: a. 22 b. 23 c. 60 d. 61

c. 60

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.) Select one: a. 0.000 b. 0.4931 c. 0.0069 d. 0.9931

c. 0.0069

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 Select one: a. 0.4332 b. 0.9332 c. 0.0668 d. 0.5668

c. 0.0668

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 Select one: a. 0.8633 b. 0.6900 c. 0.0819 d. 0.0345

c. 0.0819

Exhibit 6-5 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? Select one: a. 0.3413 b. 0.8413 c. 0.1587 d. 0.5000

c. 0.1587

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) Select one: a. 300 b. approximately 300 c. 0.75 d. 0.25

c. 0.75

Exhibit 6-5 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. Select one: a. 46.78% b. 96.78% c. 3.22% d. 53.22%

c. 3.22%

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

c. 36 and 1.86

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of is Select one: 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. approximately normal if np ≥ 5 and n(1-p) ≥ 5

Excel's NORM.DIST function can be used to compute Select one: 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. cumulative probabilities for a normally distributed x value

As the sample size increases, the Select one: 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

c. standard error of the mean decreases

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

d. 0.071 to 0.129

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 Select one: a. 7.50 b. 0.39 c. 2.00 d. 0.20

d. 0.20

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 Select one: a. 80.83 b. 7 c. 0.8083 d. 1.611

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. If we want to determine a 95% confidence interval for the average hourly income, the value of "t" statistics is Select one: a. 1.96 b. 1.64 c. 1.28 d. 1.993

d. 1.993

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

d. 170.2 to 189.8

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 Select one: 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. 8.61 to 9.39 hours

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 Select one: a. 0.5228 b. 0.9772 c. 0.4772 d. 0.0228

d. 0.0228

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 Select one: a. 0.0016 b. 0.2400 c. 0.1600 d. 0.0400

d. 0.0400

Exhibit 6-5 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. Select one: a. 0.4772 b. 0.4332 c. 0.9104 d. 0.0440

d. 0.0440

Exhibit 6-5 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? Select one: a. 0.1145 b. 0.2881 c. 0.1736 d. 0.4617

d. 0.4617

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 Select one: a. 500 and 0.047 b. 500 and 0.050 c. 0.5 and 0.047 d. 0.5 and 0.050

d. 0.5 and 0.050

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.) Select one: a. 0.0222 b. 0.4190 c. 0.5222 d. 0.9190

d. 0.9190

Exhibit 6-5 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. Select one: a. 0.5 b. 1.0 c. 0.3413 d. None of the alternative answers is correct.

d. None of the alternative answers is 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. Select one: a. ​Predictable b. ​Precise c. ​Symmetric d. Unbiased

d. Unbiased

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) Select one: a. is 14 b. is 15 c. is 15.1581 d. could be any value

d. could be any value

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

d. standard error of the proportion

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