Stats Exam#2

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

0.419 to 0.481 Correct

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

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

0.75

Greater than= (type B question)

1-

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

170.2 to 189.8

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

24.4 to 25.6

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%

3.22%

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 Correct d. 30 to 50

39.14 to 42.36 Correct

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 Correct d. 61

60 Correct

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

8.61 to 9.39 hours

Z score

= the number you were given-mean / 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 a. 0 b. .0495 c. .4505 d. None of the alternative answers is correct.

b. .0495 Correct

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

b. 1.22

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 standard deviation is (Hint: page 16 of ppt file)

b. 1.581

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 Correct d. 0.05

c. 0.9 Correct

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

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 . 0.4332 b. 0.9332 c. 0.0668 d. 0.5668

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

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

c. 0.1587

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

c. 36 and 1.86 Correct

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. Approximately 50%

In the graph below, which distribution shows the smallest standard deviation? a. Distribution I b. Distribution II c. Distribution III d. They have the same standard deviation

c. Distribution III

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 Correct c. the variance of the population is known d. the standard deviation of the population is known

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

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

is 14

Standard error =

number of people in the (category) sample / number of people in the sample

less than = (type A question)

the answer you find on the chart

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

. 0.5 and 0.050

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

. standard error of the mean decreases Correct

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 Correct

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 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 Correct

0.071 to 0.129 Correct

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 Correct b. 1.96 c. 0.20 d. 1.64

0.39 Correct

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

a. 0.000 Correct

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

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 a. 0.1359 b. 0.8185 c. 0.3413 d. 0.4772

a. 0.1359

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

a. 1.08

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. all values in an interval or collection of intervals

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.

a. central limit theorem Correct

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. is a continuous probability distribution

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

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

a. the weight of items produced by a machine

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. a mean of 0 and a standard deviation of 1

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

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

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 a. becomes larger b. becomes smaller c. stays the same d. becomes negative

becomes smaller Correct

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 Correct c. does not change d. remains the same

becomes wider 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 confidence interval based on the sample with the small standard deviation would be wider. b. The two samples would produce identical values for the lower and upper bounds of the two confidence intervals. c. None of these options is correct d. The two confidence intervals would have the same width because they are both 95% intervals.

c. None of these options is correct Correct

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

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

c. cumulative probabilities for a normally distributed x value

Assignment 5

chapter 7

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

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 (Hint: page 16 of ppt file) Select one: a. is 14 b. is 15 c. is 15.1581 d. could be any value

could be any value. because we don't know the whole population since it's infinite. Answer: could be any value

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

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 a. 80.83 b. 7 c. 0.8083 d. 1.611 Correct

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

d. 1.993

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

d. 0.0400

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

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 percentage of items will weigh between 6.4 and 8.9 ounces? a. 0.1145 b. 0.2881 c. 0.1736 d. 0.4617

d. 0.4617

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

d. 0.9190

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

d. standard error of the proportion Correct

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

d. the normally distributed x value given a cumulative probability

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 Correct 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

the size of the confidence interval to increase