Business Stats-Stats 2300-Pedram Jahangary
The probability of making a Type I error is denoted by _____. a. β b. 1 − α c. 1 − β d. α
α
If a random variable can assume one of five outcomes and the distribution is uniform, what is the probability function for this random variable? a. f(x) = .20 b. f(x) = x c. f(x) = 5 d. f(x) = 1/5x
f(x) = .20
A Type II error is committed when _____. a. a true null hypothesis is mistakenly rejected b. a true alternative hypothesis is mistakenly rejected c. the sample size has been too small d. not enough information has been available
a true alternative hypothesis is mistakenly rejected
In hypothesis testing, the critical value is _____. a. the probability of a Type II error b. a number that establishes the boundary of the rejection region c. the probability of a Type I error d. the same as the p-value
a number that establishes the boundary of the rejection region
Cluster sampling is _____. a. the same as convenience sampling b. a nonprobability sampling method c. a probability sampling method d. None of these answers are correct.
a probability sampling method
If the coefficient of determination is equal to 1, then the coefficient of correlation _____. a. must be -1 b. can be any value between -1 and 1 c. can be either -1 or 1 d. must also be equal to 1
can be either -1 or 1
In hypothesis testing, the alternative hypothesis is _____. a. the maximum probability of a Type I error b. the hypothesis concluded to be true if the null hypothesis is rejected c. the hypothesis tentatively assumed true in the hypothesis-testing procedure d. All of these answers are correct.
the hypothesis concluded to be true if the null hypothesis is rejected
The standard deviation of p̄ is referred to as the _____. a. standard error of the proportion b. average proportion c. sample proportion d. standard proportion
standard error of the proportion
The graph below best exemplifies a _____. (dollar graph) (Graph courtesy of Robert Allison.) a. bar graph b. line graph c. time series graph d. cross-sectional graph
time series graph
For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test _____. a. will result in the rejection region being smaller b. will result in the rejection region being larger c. would have no effect on the rejection region d. Not enough information is given to answer this question.
will result in the rejection region being smaller
Which of the following is not a required condition for a discrete probability function? a. Σf(x) = 0 b. Σf(x) = 1 c. f(x) ≥ 0 for all values of x d. All of these choices are correct.
Σf(x) = 0
In order to test the hypotheses H: μ ≤ 100 and H: μ > 100 at an α level of significance, the null hypothesis will be rejected if the test statistic z is _____. a. < zα b. ≥ zα c. ≤ -zα d. < 100
≥ zα
Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .9370? a. .8264 b. - 1.53 c. 1.96 d. 1.50
- 1.53
Exhibit 14-2 You are given the following information about x and y. x y Independent Dependent Variable Variable 15 5 12 7 10 9 7 11 Refer to Exhibit 14-2. The sample correlation coefficient equals _____. a. .99705 b. -86.667 c. .9941 d. -.99705
-.99705
Exhibit 14-2 You are given the following information about x and y. x y Independent Dependent Variable Variable 15 5 12 7 10 9 7 11 Refer to Exhibit 14-2. The least squares estimate of b equals _____. a. 21.4 b. -0.13 c. 16.412 d. -0.7647
-0.7647
Exhibit 9-5 n = 16 H: μ ≥ 80 x̄ = 75.607 H: μ < 80 σ = 8.246 Assume the population is normally distributed.The test statistic equals _____. a. .53 b. 2.131 c. -.53 d. -2.131
-2.131
Suppose a person will purchase a new vehicle within the next six months with a probability of .35. If the probability that a person will receive a raise within the next six months is .20, what is the probability that a person purchases a new vehicle and receives a raise within the next six months? Assume the two events are independent. a. .93 b. .55 c. .07 d. 1
.07
If A and Bare mutually exclusive events with P(A) = .45 and P(B) = .05, what is P(A U B)? a. .40 b. .95 c. .50 d. Not enough information is given to answer this question.
.50
In a regression analysis, if SSE = 200 and SSR = 300, then the coefficient of determination is _____. a. 1.500 b. .400 c. .667 d. .600
.600
Exhibit 14-4 The following information regarding a dependent variable (y) and an independent variable (x) is provided. x y 2 4 1 3 4 4 3 6 5 8 SSE = 6 SST = 16 Refer to Exhibit 14-4. The coefficient of determination is _____. a. -.7906 b. .375 c. .625 d. .7096
.625
The prior probabilities for events A and A are P(A) = .25 and P(A) = .75. The conditional probabilities of event B given A and A are P(B | A) = .45, and P(B | A) = .30. Using Bayes' theorem, what is the posterior probability P(A | B)? a. .667 b. .225 c. .338 d. .775
.667
Exhibit 14-4 The following information regarding a dependent variable (y) and an independent variable (x) is provided. x y 2 4 1 3 4 4 3 6 5 8 SSE = 6 SST = 16 Refer to Exhibit 14-4. The coefficient of correlation is _____. a. -.7906 b. .7906 c. .375 d. .625
.7906
Exhibit 14-2 You are given the following information about x and y. x y Independent Dependent Variable Variable 15 5 12 7 10 9 7 11 Refer to Exhibit 14-2. The coefficient of determination equals _____. a. -.9941 b. .9941 c. .99705 d. -.99705
.9941
In a multiple regression model, the error term ε is assumed to be a random variable with a mean of _____. a. −1 b. 0 c. 1 d. any value
0
If A and B are mutually exclusive events with P(A) = 0.2 and P(A∪B) =.45, what is P(B)? a. Not enough information is given to answer this question. b. 0.65 c. 0.25 d. 0
0.25
What is the probability that a randomly selected customer pays either with cash or check?P(A∪B) =? a. 0.3 b. 0.05 c. 0.25 d. 0.35
0.35
The prior probabilities for events B1 and B2 are P(B1) = 0.2 and P(B2) = 0.6. The conditional probabilities of event A given B1 and B2 are P(A|B1) = 0.3, and P(A|B2) = 0.4. Using Bayes' theorem, what is the posterior probability P(B2|A)? a. 0.2 b. 0.8 c. 0.4 d. 2.5
0.8
Exhibit 14-4 The following information regarding a dependent variable (y) and an independent variable (x) is provided. x y 2 4 1 3 4 4 3 6 5 8 SSE = 6 SST = 16 Refer to Exhibit 14-4. The least squares estimate of the slope is _____. a. 1 b. 3 c. 4 d. 2
1
Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.Refer to Exhibit 8-3. The value to use for the standard error of the mean is _____. a. 1.5 b. 2.26 c. 13.5 d. 9
1.5
To test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____. a. 255 and 14 b. 13 and 240 c. 14 and 240 d. 14 and 255
14 and 240
There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement)that are possible equals _____. a. 3 b. 12 c. 16 d. 15
15
Exhibit 15-2 A regression model between sales (y in $1000s), unit price (x in dollars) and television advertisement (x in dollars) resulted in the followingfunction: ŷ = 7 − 3x + 5x For this model, SSR = 3500, SSE = 1500, and the sample size is 18. If SSR = 600 and SSE = 300, the test statistic F is _____. a. 1.75 b. 17.5 c. 2.33 d. .70
17.5
A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8.The 95.44% confidence interval for the population mean is _____. a. 19.2 to 20.8 b. 15.2 to 24.8 c. 19.216 to 20.784 d. 21.2 to 22.8
19.2 to 20.8
Exhibit 14-4 The following information regarding a dependent variable (y) and an independent variable (x) is provided. x y 2 4 1 3 4 4 3 6 5 8 SSE = 6 SST = 16 Refer to Exhibit 14-4. The MSE is _____. a. 4 b. 1 c. 3 d. 2
2
Exhibit 14-4 The following information regarding a dependent variable (y) and an independent variable (x) is provided. x y 2 4 1 3 4 4 3 6 5 8 SSE = 6 SST = 16 Refer to Exhibit 14-4. The least squares estimate of the y-intercept is ______. a. 4 b. 1 c. 3 d. 2
2
Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. ANOVA df SSMSFRegression4,8532,426.5Residual485.3CoefficientsStandard ErrorIntercept12.9244.425x-3.6822.630x45.21612.560 The degrees of freedom for the sum of squares explained by the regression (SSR) are _____. a. 13 b. 3 c. 2 d. 15
2
Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. The test statistic is _____. a. .056 b. 1.96 c. 2.00 d. 1.64
2.00
Exhibit 9-4 A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. The test statistic is _____. a. 1.645 b. 2.00 c. .05 d. 1.96
2.00
Exhibit 14-3 Regression analysis was applied between sales data (in $1000s) and advertising data (in $100s), and the following information was obtained. ŷ = 12 + 1.8xn = 17 SSR = 225 SSE = 75 S = 0.2683 Refer to Exhibit 14-3. Using α = .05, the critical t value for testing the significance of the slope is _____. a. 2.120 b. 1.753 c. 1.746 d. 2.131
2.131
Exhibit 9-1 n = 36H: μ≤ 20 x̄ = 24.6H: μ> 20 σ = 12 The test statistic equals _____. a. 2.3 b. -.38 c. .38 d. -2.3
2.3
Given that z is a standard normal random variable, what is the value of z such that P(Z≥z) = 0.01? (Hint:what is the value of z if the area to the right of z is only .01? ) a. 0.01 b. 0.99 c. 2.32 d. -2.32
2.32
Exhibit 15-5 Below is a partial Excel output based on a sample of 25 observations. 145.321 48.682 25.625 9.150 −5.720 3.575 0.823 0.183 We want to test whether the parameter β is significant. The test statistic equals _____. a. 14 b. .357 c. 1.96 d. 2.8
2.8
Five individuals attend a Machine learning class. Two individuals are selected from the class to make a pre-sentation for half an hour. In how many ways can the two individuals be selected i fordering is important? a. 10 b. 20 c. 15 d. 60
20
Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained: ŷ = 29 + 18x + 43x + 87x For this model, SSR = 600 and SSE = 400. The computed F statistic for testing the significance of the above model is _____. a. 1.500 b. 20.00 c. .600 d. .6667
20.00
Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained: ŷ = 29 + 18x + 43x + 87x For this model, SSR = 600 and SSE = 400. MSR for this model is _____. a. 10 b. 1,000 c. 200 d. 43
200
Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x) and their gender(x) (0 if male and 1 if female). ŷ = 30 + 0.7x + 3x Also provided are SST = 1200 and SSE = 384. The test statistic for testing the significance of the model is _____. a. 28.69 b. .73 c. 1.47 d. 5.22
28.69
To test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____. a. 3 and 47 b. 2 and 43 c. 3 and 43 d. 47 and 3
3 and 43
Exhibit 15-2 A regression model between sales (y in $1000s), unit price (x in dollars) and television advertisement (x in dollars) resulted in the followingfunction: ŷ = 7 − 3x + 5x For this model, SSR = 3500, SSE = 1500, and the sample size is 18. If we want to test for the significance of the regression model, the critical value of F at 95% confidence is _____. a. 3.24 b. 3.29 c. 3.68 d. 4.54
3.68
Exhibit 7-5 Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation of the sampling distribution of the sample means are _____. a. 36 and 8 b. 36 and 1.86 c. 8.7 and 1.94 d. 36 and 1.94
36 and 1.86
What percentage of the undergraduates surveyed are majoring in Engineering? a. 37.75 % b. 42 % c. 110 % d. 50 %
37.75 %
Exhibit 14-3 Regression analysis was applied between sales data (in $1000s) and advertising data (in $100s), and the following information was obtained. ŷ = 12 + 1.8xn = 17 SSR = 225 SSE = 75 S = 0.2683 Refer to Exhibit 14-3. The critical F value at α = .05 is _____. a. 4.45 b. 3.68 c. 3.59 d. 4.54
4.54
Find P(10≤x≤30) for a uniform random variable defined on the interval 10 to 55. a. 44.44 % b. 36.36 % c. 50.00 % d. 66.66 %
44.44 %
Exhibit 14-3 Regression analysis was applied between sales data (in $1000s) and advertising data (in $100s), and the following information was obtained. ŷ = 12 + 1.8xn = 17 SSR = 225 SSE = 75 S = 0.2683 Refer to Exhibit 14-3. The F statistic computed from the above data is _____. a. 45 b. 48 c. 3 d. Not enough information is given to answer this question.
45
Ten individuals attend a group ski lesson. Two individuals are selected from the group lesson to receive private lessons for a 15-minute period. In how many ways can the two individuals be selected if order is not important? a. 20 b. 45 c. 10 d. 5
45
A population consists of 8 items. The number of different simple random samples of size 3 (without replacement) that can be selected from this population is _____. a. 128 b. 24 c. 512 d. 56
56
Suppose a random variable t has a probability distribution defined by f(t) = t/20 for t = 2, 4, 6, and 8. What is the expected value for t? a. 2 b. 1.5 c. 5 d. 6
6
Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. ANOVA df SSMSFRegression4,8532,426.5Residual485.3CoefficientsStandard ErrorIntercept12.9244.425x-3.6822.630x45.21612.560 The sum of squares due to error (SSE) equals _____. a. 485.3 b. 6,308.9 c. 37.33 d. 4,853
6,308.9
Exhibit 14-3 Regression analysis was applied between sales data (in $1000s) and advertising data (in $100s), and the following information was obtained. ŷ = 12 + 1.8xn = 17 SSR = 225 SSE = 75 S = 0.2683 Refer to Exhibit 14-3. The t statistic for testing the significance of the slope is _____. a. 6.709 b. 1.80 c. 1.96 d. .555
6.709
If the coefficient of correlation is .8, then the percentage of variation in the dependent variable explained by the estimated regression equation is_____. a. 0.80% b. 64% c. 80% d. 0.64%
64%
It is known that the variance of a population equals 1,936. A random sample of 121 has been selected from the population.There is a .95 probability that the sample mean will provide a margin of error of _____. a. 31.36 or less b. 1,936 or less c. 7.84 or less d. 344.96 or less
7.84 or less
When the hypotheses H: μ ≥ 100 and H: μ < 100 are being tested at a level of significance of α, the null hypothesis will be rejected if the teststatistic z is _____. a. >zα b. < 100 c. < -zα d. > -zα
< -zα
Suppose the number of personal days an employee uses per year has a mean of 8 and a standard deviation of 2. What percent of the data values will be within two standard deviations of the mean if the distribution is bell-shaped? a. At least 30% b. At least 75% c. At least 95% d. The percentage cannot be computed with the information given.
At least 75%
A retailer received seven new items from the manufacturer. Based on historical records, the probability of observing a damaged part upon delivery is only 5%. The retailer sold three items to different customers.Which of the following probability distributions would be useful to calculate the probability of seeing all the parts were damaged? a. Hypergeometric probability distribution b. Poisson probability distribution c. Uniform probability distribution d. Binomial probability distributions
Binomial probability distributions
The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is _____. a. H: p > .30 H: p ≤ .30 b. H: p ≤ .30 H: p > .30 c. H: p < .30 H: p ≥ .30 d. H: p ≥ .30 H: p < .30
H: p ≥ .30 H: p < .30
Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____. a. H: μ < 10.0% H: μ ≥ 10.0% b. H: μ ≥ 10.0% H: μ < 10.0% c. H: μ > 10.0% H: μ ≤ 10.0% d. H: μ ≤ 10.0% H: μ > 10.0%
H: μ ≥ 10.0% H: μ < 10.0%
A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is _____. a. H: μ > 85 H: μ ≤ 85 b. H: μ ≥ 85 H: μ < 85 c. H: μ ≤ 85 H: μ > 85 d. H: μ < 85 H: μ ≥ 85
H: μ ≥ 85 H: μ < 85
A retailer received seven new items from the manufacturer. Four of the items were damaged in transit. The retailer sold three items to five customers. Which of the following probability distributions would be useful in this situation? a. Hypergeometric probability distribution b. Poisson probability distribution c. Uniform probability distribution d. Binomial probability distributions
Hypergeometric probability distribution
Excel's __________ function can be used to calculate a p-value for a hypothesis test. a. NORM.S.DIST b. RAND c. NORM.S.INV d. Not enough information is given to answer this question.
NORM.S.DIST
A newspaper wants to estimate the proportion of Americans who will vote for Candidate A. A random sample of 1000 voters is selected. Of the 1000 respondents, 526 say that they will vote for Candidate A. Which Excel function would be used to construct a confidence interval estimate? a. T.INV b. NORM.S.INV c. INT d. NORM.INV
NORM.S.INV
The ratio of MSE/MSR yields _____. a. the F statistic b. SSR c. SST d. None of these answers are correct.
None of these answers are correct.
In a multiple regression analysis, SSR = 1,000 and SSE = 200. The F statistic for this model is _____. a. 800 b. 1,200 c. 5.0 d. Not enough information is provided to answer this question.
Not enough information is provided to answer this question.
Which of the following is not true when assigning probabilities to each of n experimental outcomes in a sample space? a. P(E)+P(E) + ... +P(E) = 1 b. 0 ≤ P(E) ≤ 1 c. P(S) = 1 where Sis the sample space d. P(E) -P(E) -... -P(E) = 0
P(E) -P(E) -... -P(E) = 0
The multiple coefficient of determination is _____. a. SSE/SSR b. MSR/MSE c. SSR/SST d. MSR/MST
SSR/SST
Which of the following statements is not correct? a. The Poisson distribution provides a description of the number of occurrences per interval b. The exponential distribution provides a description of the length of the interval between occurrences c. The Poisson distribution is used for discrete and Exponential distribution is used for continuous random variables. d. The Poisson distribution provides a description of the length of the interval between occurrences
The Poisson distribution provides a description of the length of the interval between occurrences
Local residents were surveyed for their satisfaction with the local government. The responses were recorded as follows: 0-not satisfied 1-somewhat dissatisfied 2-satisfied 3-very satisfied The variable recorded is an example of what type of variable? a. Quantitative variable b. Variable measured on the ratio scale c. Variable measured on the interval scale d. Variable measured on the ordinal scale
Variable measured on the ordinal scale
The error of rejecting a true null hypothesis is _____. a. a Type II error b. committed when not enough information is available c. a Type I error d. either a Type I or Type II error, depending on the situation
a Type I error
The amount of time a patient must wait to be seen at a doctor's office is an example of a. a continuous random variable. b. either a continuous or a discrete random variable, depending on the type of doctor's office. c. either a continuous or a discrete random variable, depending on the gender of the individual. d. a discrete random variable.
a continuous random variable.
Exhibit 15-5 Below is a partial Excel output based on a sample of 25 observations. 145.321 48.682 25.625 9.150 −5.720 3.575 0.823 0.183 Carry out the test of significance for the parameter β at the 5% level. The null hypothesis should _____. a. not be rejected b. be revised c. be rejected d. None of these answers are correct.
be rejected
Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. ANOVA df SSMSFRegression4,8532,426.5Residual485.3CoefficientsStandard ErrorIntercept12.9244.425x-3.6822.630x45.21612.560 Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should ______. a. be rejected b. be revised c. not be rejected d. None of these answers are correct.
be rejected
Exhibit 9-1 n = 36H: μ≤ 20 x̄ = 24.6H: μ> 20 σ = 12 If the test is done at a .05 level of significance, the null hypothesis should _____. a. be rejected b. not be rejected c. Not enough information is given to answer this question. d. None of these answers are correct.
be rejected
The numerical value of the coefficient of determination _____. a. is always smaller than the coefficient of correlation b. is always larger than the coefficient of correlation c. can be larger or smaller than the coefficient of correlation d. is negative if the coefficient of determination is negative
can be larger or smaller than the coefficient of correlation
Which of the following sampling methods does NOT lead to probability samples? a. systematic sampling b. cluster sampling c. convenience sampling d. stratified sampling
convenience sampling
To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT _____. a. population standard deviation b. desired margin of error c. confidence level d. degrees of freedom
degrees of freedom
For a two-tailed hypothesis test about a population mean, the null hypothesis can be rejected if the confidence interval _____. a. includes μ b. is symmetric c. does not include μ d. is non-symmetric
does not include μ
If the coefficient of correlation is .4, the percentage of variation in the dependent variable explained by the estimated regression equation _____. a. is 16% b. can be any positive value c. is 40% d. is 4%
is 16%
The rejection region for a one-tailed hypothesis test_____. a. has an area equal to the confidence coefficient b. is in the tail that supports the alternative hypothesis c. has an area of 1 - β d. is in the tail that supports the null hypothesis
is in the tail that supports the alternative hypothesis
All of the following are true about the standard error of the mean EXCEPT _____. a. it decreases as the sample size increases b. it is larger than the standard deviation of the population c. it measures the variability in sample means d. its value is influenced by the standard deviation of the population
it is larger than the standard deviation of the population
When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve _____. a. greater than or equal to the critical value b. less than or equal to the test statistic c. less than or equal to the critical value d. greater than or equal to the test statistic
less than or equal to the test statistic
In a two-tailed hypothesis test, the null hypothesis should be rejected if the p-value is _____. a. less than or equal to α b. less than or equal to 2α c. greater than or equal to α d. greater than or equal to 2α
less than or equal to α
The level of significance is the _____. a. same as the p-value b. same as the confidence coefficient c. maximum allowable probability of a Type II error d. maximum allowable probability of a Type I error
maximum allowable probability of a Type I error
The least squares criterion is _____. a. min (Σy - ŷ) b. min Σ(y - ŷ) c. min Σ(x - y) d. min Σ(y - ȳ)
min Σ(y - ŷ)
Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be _____. a. the same b. Not enough information is given. c. narrower d. wider
narrower
Exhibit 9-3 n = 49 H: μ = 50 x̄ = 54.8 H: μ ≠ 50 σ = 28 If the test is done at a 5% level of significance, the null hypothesis should _____. a. be rejected b. not be rejected c. Not enough information is given to answer this question. d. None of these answers are correct.
not be rejected
Exhibit 9-4 A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. At a .05 level of significance, it can be concluded that the mean age is _____. a. significantly less than 25 b. not significantly different from 24 c. significantly different from 24 d. significantly less than 24
not significantly different from 24
As a general rule, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever _____. a. n(1 − p) ≥ 5 b. np ≥ 5 c. n ≥ 30 d. np ≥ 5 and n(1 − p) ≥ 5
np ≥ 5 and n(1 − p) ≥ 5
We can use the normal distribution to make confidence interval estimates for the population proportion, p, when _____. a. np ≥ 5 b. p has a normal distribution c. np ≥ 5 and n(1 − p) ≥ 5 d. n(1 − p) ≥ 5
np ≥ 5 and n(1 − p) ≥ 5
A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of x̄ is approximately normal because _____. a. x̄ is always approximately normally distributed b. of the central limit theorem c. the sample size is small in comparison to the population size d. None of these answers are correct.
of the central limit theorem
Exhibit 8-2 The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. Refer to Exhibit 8-2. If the confidence coefficient is reduced to .80, the standard error of the mean _____. a. will decrease b. becomes negative c. will increase d. remains unchanged
remains unchanged
In determining the sample size necessary to estimate a population proportion, which of the following is NOT needed? a. the mean of the population b. the maximum margin of error that can be tolerated c. the confidence level required d. a preliminary estimate of the true population proportion p
the mean of the population
As the goodness of fit for the estimated multiple regression equation increases, _____. a. the value of the regression equation's constant b decreases b. the value of the multiple coefficient of determination increases c. the value of the adjusted multiple coefficient of determination decreases d. the value of the correlation coefficient increases
the value of the multiple coefficient of determination increases
