Quantitative Business Analysis: Exercises 5 to 8 (Quality Answers Only)

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Exercise 5

From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is ____.

 a

15

 b

2

 c

3.92

 d

4

Question 2 (1 point)

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

Question 3 (1 point)

The farther the sample mean is from the population mean ___.

 a

the larger the sampling error

 b

the smaller the sampling error

 c

the likelier it is that the sampling error equals 1

 d

none of the above

Question 4 (1 point)

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12, respectively. The standard error of the mean is ____.

 a

1.20

 b

0.12

 c

8.00

 d

0.80

Question 5 (1 point)

If an interval estimate is said to be constructed at the 99% confidence level, the confidence coefficient would be ____.

 a

0.1

 b

0.99

 c

0.9

 d

0.05

Question 6 (1 point)

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

Question 7 (1 point)

A simple random sample was taken from a large normal population. The sample mean and the population standard deviation were determined to be 80 and 12, respectively. What random sample size is needed to determine within +/-2 the true population mean within a 99% confidence?

 a

229

 b

16

 c

impossible to determine

 d

239

Question 8 (1 point)

The closer the sample mean is to the population mean, ____.

 a

the larger the sampling error

 b

the smaller the sampling error

 c

the sampling error equals 1

 d

none of the above

Question 9 (1 point)

From a population with a variance of 625, a sample of 625 items is selected. At 95% confidence, the margin of error is approximately ___.

 a

15

 b

2

 c

3.92

 d

1

Question 10 (1 point)

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of a particular element being selected is ___.

 a

0.100

 b

0.010

 c

0.001

 d

0.002

Exercise6

Question 1 (1 point)

For a two-tailed test at 96.12% confidence, z = _____.

 a

+/-1.96

 b

+/-1.48

 c

+/-1.09

 d

+/-2.07

Question 2 (1 point)

A two-tailed t-test is performed at an alpha = 0.01. The sample mean was 11 the random sample size was 25, and the sample variance is 16. You are testing whether the sample mean is significantly different from the population mean of 12. You conclude: ______.

 a

you should accept the alternate hypothesis (is significantly less)

 b

there is not enough data

 c

the null hypothesis could not be rejected

 d

the analysis has been designed incorrectly

Question 3 (1 point)

An assumption made about the value of a population parameter is called a ____.

 a

hypothesis

 b

conclusion

 c

confidence

 d

significance

Question 4 (1 point)

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

H0: μ < 85; Ha: μ ≥ 85

 b

H0: μ < 85; Ha: μ ≥ 85

 c

H0: ≥ 85; Ha: μ < 85

 d

H0: μ > 85; Ha: μ ≤ 85

Question 5 (1 point)

What type of error occurs if you fail to reject H0 when, in fact, it is not true?

 a

Type II

 b

Type I

 c

either Type I or Type II, depending on the level of significance

 d

either Type I or Type II, depending on whether the test is one tail or two tail

Question 6 (1 point)

In hypothesis testing, if the null hypothesis is rejected, ______.

 a

no conclusions can be drawn from the test

 b

the alternative hypothesis is false

 c

the data must have been accumulated incorrectly

 d

none of the above

Question 7 (1 point)

For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.064. If the test is being conducted at 95% confidence, the null hypothesis ______.

 a

could be rejected or not rejected depending on the sample

 b

could be rejected or not rejected depending on the value of the mean of the sample

 c

is not rejected

 d

is rejected

Question 8 (1 point)

In hypothesis testing, if the null hypothesis is not rejected, ______.

 a

no conclusions can be drawn from the test

 b

the alternative hypothesis is false

 c

the data collected is not random

 d

the sample size was too small

Question 9 (1 point)

An upper one-tailed z-test is performed at an alpha = 0.02. The sample percentage was 20% and the random sample size was 200. You are testing whether the sample percentage is significantly more than the population of 15%. You conclude: _______.

 a

you should accept the alternate hypothesis (is significantly less)

 b

there is not enough data

 c

the null hypothesis could not be rejected

 d

the analysis has been designed incorrectly

Question 10 (1 point)

For a two-tailed test at 86.12% confidence, z = ______.

 a

+/- 1.96

 b

+/- 1.48

 c

+/- 1.09

 d

+/- 0.86

Exercise 7

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have approximately equal variances, we must use a t-distribution with (let n1 be the size of sample 1 and n2 the size of sample 2) degrees-of-freedom.

 a

(n1 + n2) degrees of freedom

 b

(n1 + n2 - 1) degrees of freedom

 c

(n1 + n2 - 2) degrees of freedom

 d

n1 - n2 + 2

Question 2 (1 point)

An important application of the chi-square distribution is _____.

 a

making inferences about a single population variance

 b

testing for goodness-of-fit

 c

testing for the independence of two variables

 d

all of the above

Question 3 (1 point)

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be statistically equal. The sample sizes are n1= 55 and n2= 45. The correct distribution to use is the ____.

 a

t -distribution with 101 degrees of freedom

 b

t- distribution with 99 degrees of freedom

 c

t -distribution with 100 degrees of freedom

 d

t -distribution with 98 degrees of freedom

Question 4 (1 point)

In a one-tailed (upper tail) hypothesis test the test statistic is determined to be z = 2.5. The p-value for this test _____.

 a

is 0.0062

 b

is 0.0124

 c

is 0.4938

 d

0.9938

Question 5 (1 point)

The chi-square procedure is a statistical approach particularly useful for ____.

 a

analyzing surveys

 b

evaluating goodness-of-fit

 c

testing for independence

 d

all of the above

Question 6 (1 point)

In a one-tailed (upper tail) hypothesis test the test statistic is determined to be z = 2.20. The p-value for this test is ______.

 a

0.0139

 b

0.0124

 c

0.4938

 d

0.9861

Question 7 (1 point)

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have statistically equal variances, we must use a t-distribution with (let n1be the size of sample 1 and n2the size of sample 2) degrees-of-freedom _____.

 a

(n1 - n2) degrees- of- freedom

 b

(n1 - n2 - 1) degrees- of- freedom

 c

none of these answers

 d

(n1 - n2 + 1) degrees- of- freedom

Question 8 (1 point)

A friend argues that both a two-sample t-test hypotheses test and ANOVA can be used for a two- sample problem. You said _____.

 a

different tests, different results

 b

this is a true statement

 c

it depends on sample sizes

 d

it depends on the variances

Question 9 (1 point)

In the chi-square test of independence you determined that the test statistic to be 5.551. You have four columns and three rows of data, and you are testing at an alpha of 0.05. Your decision is ____.

 a

that the population data is independent

 b

that the population data is dependent

 c

impossible to tell

 d

none of the above

Question 10 (1 point)

If a hypothesis is rejected at 95% confidence, _____.

 a

it must also be rejected at the 99% confidence

 b

it must also be rejected at the 90% confidence

 c

it will sometimes be rejected and sometimes not be rejected at the 90% confidence

 d

not enough information is given to answer this question

Exercise 8

Question 1 (1 point)

Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained. http://www.schoology.com/system/files/attachments/page_embeds/m/2014-11/image0035464ede8_5464f32d8fa1f.gif Based on the above estimated regression equation, if price is increased by two units, then demand is expected to _____.

 a

increase by 120 units

 b

increase by 100 units

 c

increase by 20 units

 d

decease by 20 units

Question 2 (1 point)

If the coefficient of correlation is a positive value, then the regression equation _____.

 a

must have a positive slope

 b

must have a negative slope

 c

could have either a positive or a negative slope

 d

must have a positive y intercept

Question 3 (1 point)

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is __.

 a

0.6667

 b

0.6000

 c

0.4000

 d

1.5000

Question 4 (1 point)

In regression analysis, the model in the form http://www.schoology.com/system/files/attachments/page_embeds/m/2014-11/image0025464ede8_5464f32d78372.gifis called _____.

 a

regression equation

 b

correlation equation

 c

estimated regression equation

 d

regression model

Question 5 (1 point)

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called ______.

 a

the correlation model

 b

the regression model

 c

correlation analysis

 d

none of the above

Question 6 (1 point)

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1= 25 and n2= 35. The correct distribution to use is the ____.

 a

t distribution with 61 degrees of freedom

 b

t distribution with 60 degrees of freedom

 c

t distribution with 59 degrees of freedom

 d

t distribution with 58 degrees of freedom

Question 7 (1 point)

The standard error is the ______

 a

variance of http://www.schoology.com/system/files/attachments/page_embeds/m/2014-11/image0045464ede8_5464f32dc86c4.gif

 b

variance of the sampling distribution of http://www.schoology.com/system/files/attachments/page_embeds/m/2014-11/image0045464ede8_5464f32dec4fc.gif

 c

standard deviation of the sampling distribution of http://www.schoology.com/system/files/attachments/page_embeds/m/2014-11/image0045464ede8_5464f32e0acfb.gif

 d

difference between the two means

Question 8 (1 point)

If a hypothesis is rejected at 95% confidence, _____.

 a

it must also be rejected at the 99% confidence

 b

it must also be rejected at the 90% confidence

 c

it will sometimes be rejected and sometimes not be rejected at the 90% confidence

 d

Not enough information is given to answer this question.

Question 9 (1 point)

Correlation analysis is used to determine _____.

 a

the equation of the regression line

 b

the strength of the relationship between the dependent and the independent variables

 c

a specific value of the dependent variable for a given value of the independent variable

 d

none of the above

Question 10 (1 point)

In regression and correlation analysis, if SSE and SST are known, then with this information the ____.

 a

coefficient of determination can be computed

 b

slope of the line can be computed

 c

Y intercept can be computed

 d

x intercept can be computed