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Statistics, section 2, Fall 2019
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OpenStax - Intro to Business Statistics 1/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 30 / 69

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving... ()

Ask Your Teacher Extension Requests Print Assignment

Question

Points

1	2	3	4	5	6	7	8	9
6/6	12/14	4/10	–/9	8/13	–/2	–/6	0/6	0/3

Total

30/69 (43.5%)

Instructions

Cengage is proud to support the open source teaching community. Introductory Business Statistics, authored by Alexander Holmes, Barbara Illowsky, and Susan Dean, is available through OpenStax and is now supported by homework questions and student learning resources within WebAssign.

Question 1 exemplifies submitting an incorrect response, and settings can allow students to have rhetorical guidance on answering the question.

Question 2 contains an image with answer blanks included for a seamless experience for the student.

Question 3 is a multipart question in which students are asked to analyze the given information to determine the necessary distribution and then use that distribution to determine probabilities.

Question 4 is a multipart question that uses multiple answer types for students to graph the probability distribution, derive its formula, and then use that formula to determine probabilities.

Question 5 utilizes multiple answer types to determine probability statements, graph the respective areas, and then determine probabilities.

Question 6 links to appendix tables and a distribution calculator to construct a confidence interval.

Question 7 guides students through a hypothesis test using the student's t distribution.

Question 8 steps students through a hypothesis test using the Chi-Square distribution.

Question 9 showcases the use of some values from an ANOVA table to calculate the F-test statistic. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 6/6 points | Previous Answers OSIntroBusStat1 1.1.002.HW. My Notes

2. 12/14 points | Previous Answers OSIntroBusStat1 3.5.122.HW. My Notes

A box of cookies contains 2 chocolate and 8 butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?)

(a)

Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree. (Let B be the event that he selected a butter cookie, and let C be the event that he selected a chocolate cookie. Enter your probabilities as fractions.)

Tree Diagram

WebAssign Plot — A tree diagram has 6 answer blanks. Refer to the adjacent tab for a description.

Incorrect: Your answer is incorrect. — A tree diagram has 6 answer blanks. Refer to the adjacent tab for a description.

Description

A tree diagram begins at a point. A left and right branch extend down from this initial point. From each of these two branches, a left and right branch extend down. From each of these four branches a single branch extends down.
The branches extending from the initial point from left to right are labeled B and C. An answer blank is placed along each of these branches.
The branches extending from the point at the end of the branch labeled B from left to right are labeled B and C. An answer blank is placed along each of these branches.
The branches extending from the point at the end of the branch labeled C from left to right are labeled B and C. An answer blank is placed along each of these branches.
A branch labeled BB extends from the branch labeled B that extended from the branch labeled B that began at the initial point.
A branch labeled BC extends from the branch labeled C that extended from the branch labeled B that began at the initial point.
A branch labeled CB extends from the branch labeled B that extended from the branch labeled C that began at the initial point.
A branch labeled CC extends from the branch labeled C that extended from the branch labeled C that began at the initial point.

(b)

Are the probabilities for the flavor of the SECOND cookie that Miguel selects independent of his first selection? Explain.

The probabilities for the second cookie selection are independent of the first selection. The cookies are replaced after selecting them. The probabilities for the second cookie selection are independent of the first selection. The cookie that was selected first has no impact on the probability of selecting a particular cookie type on the second selection. correct

The probabilities for the second cookie selection are dependent on the first selection. The probability of a chocolate cookie being selected second is dependent on whether a chocolate or butter cookie was selected first. The probabilities for the second cookie selection are dependent on the first selection. The probability of selecting a chocolate cookie second is the same as selecting a butter cookie.

Incorrect. The selections are done without replacement which means the first selection affects the second.

(c)

For each complete path through the tree, write the event it represents and find the probabilities. (Enter your probabilities as fractions.)

P(BB)	=	28/45
P(BC)	=	8/45
P(CB)	=	8/45
P(CC)	=	1/45

(d)

Let S be the event that both cookies selected were the same flavor. Find P(S). (Enter your probability as a fraction.)

29/45

(e)

Let T be the event that both cookies selected were different flavors. Find P(T) by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods. (Enter your probability as a fraction.)

16/45

(f)

Let U be the event that the second cookie selected is a butter cookie. Find P(U). (Enter your probability as a fraction.)

4/5

†

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3. 4/10 points | Previous Answers OSIntroBusStat1 4.2.065.HW. My Notes

More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 12 such institutions. We are interested in the number that offer distance learning courses.

Part (a)

In words, define the Random Variable X.

the number of distance learning courses offered at each college or university the number of colleges and universities in the United States the number of colleges and universities that offer distance learning courses the percentage of colleges and universities that offer distance learning courses

Correct! This is a numerical measure of the outcome of the study.
Part (b)

List the values that X may take on.

X = 0, 1, 2, . . ., 10, 11, 12 X = 1, 2, 3, . . ., 10, 11, 12 X = 1, 2, 3, . . ., 95, 96 X = 0, 1, 2, 3, . . ., 95, 96
Part (c)

Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.)
X ~
B

12
,
0.96
Part (d)

On average, how many schools would you expect to offer such courses? (Round your answer to the nearest whole number.)

12
schools
Part (e)

Find the probability that at most nine offer such courses. (Round your answer to four decimal places.)

0.0107
Part (f)

Is it more likely that 11 or that 12 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.
The probability that 11 schools will offer such courses is and the probability that 12 schools will offer such courses is . Therefore, it is more likely that schools will offer distance learning courses.

†

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4. –/9 points OSIntroBusStat1 5.2.073.HW. My Notes

For each probability and percentile problem, draw the picture.

A random number generator picks a number from 2 to 8 in a uniform manner.

(a)

Graph the probability distribution.

A graph has a horizontal axis labeled x with values from 0 to 9 and the vertical axis is labeled f(x) with values from 0 to 0.17. The curve begins at the point (2, 0), goes vertically up, changes direction at the approximate point (2, 0.10), goes horizontally right, changes directions at the approximate point (8, 0.10), goes vertically down, and ends at the point (8, 0).

(b)

Find

f(x).

f(x) =

, where ≤ x ≤

(c)

Find μ.

μ =

(d)

Find σ. (Round your answer to two decimal places.)

σ =

(e)

Find P(3.75 < x < 7.5). (Enter your answer as a fraction.)

P(3.75 < x < 7.5) =

(f)

Find P(x > 4.33). (Round your answer to two decimal places.)

P(x > 4.33) =

(g)

Find P(x > 6 | x > 5). (Enter your answer as a fraction.)

P(x > 6 | x > 5) =

†

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5. 8/13 points | Previous Answers OSIntroBusStat1 6.3.077.HW. My Notes

You may need to use the appropriate appendix table or technology to answer this question.

According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual.

(a)

Give the distribution of X.

X ~

2.5

(b)

Find the probability that the person is between 64 and 69 inches.

Write the probability statement.

< X <

What is the probability? (Round your answer to four decimal places.)

0.6731

Sketch the graph.

A graph has a horizontal axis labeled X with values from 54 to 78 and a vertical axis with values from 0 to 0.17. The curve enters the window from the left, at a height of nearly zero above the horizontal axis, goes up and to the right, changes direction at approximately (66, 0.16), and then goes down and to the right before exiting the window at a height of nearly zero above the horizontal axis. The area under the curve to the left of 64 as well as the area under the curve to the right of 69 are both shaded.

(c)

Would you expect to meet many Asian adult males over 74 inches? Explain why or why not, and justify your answer numerically.

, because the probability that an Asian male is over 74 inches tall is .

(d)

The middle 40% of heights fall between what two values?

Write the probability statement.

P(x₁ < X < x₂) =

0.4

State the two values. (Round your answers to two decimal places.)

x₁ =

64.69

x₂ =

67.31

Sketch the graph.

†This work is a derivative of a text by OpenStax, used under CC BY by Cengage, Inc.

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6. –/2 points OSIntroBusStat1 8.2.107.HW. My Notes

You may need to use the appropriate appendix table or technology to answer this question.

The Federal Election Commission (FEC) collects information about campaign contributions and disbursements for candidates and political committees each election cycle. A political action committee (PAC) is a committee formed to raise money for candidates and campaigns. A Leadership PAC is a PAC formed by a federal politician (senator or representative) to raise money to help other candidates' campaigns.

The FEC has reported financial information for 556 Leadership PACs that operated during one election cycle. The following table shows the total receipts during this cycle for a random selection of 30 Leadership PACs.

$46,502.00	$0	$40,965.50	$105,886.20	$5,176.00
$29,048.00	$19,499.00	$181,556.20	$31,499.00	$149,972.80
$2,555,362.20	$12,026.00	$409,001.00	$60,520.70	$17,999.00
$61,809.20	$76,529.80	$119,461.20	$0	$63,521.00
$6,499.00	$502,580.00	$705,062.10	$708,259.90	$135,809.00
$1,998.00	$2,002.00	$0	$1,287,934.80	$219,147.30

x = $251,854.23 s = $521,130.50

Use this sample data to construct a 95% confidence interval for the mean amount of money (in dollars) raised by all Leadership PACs during the election cycle. Use the Student's t-distribution. (Round your answers to the nearest cent.)

dollars

†This work is a derivative of a text by OpenStax, used under CC BY by Cengage, Inc.

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7. –/6 points OSIntroBusStat1 9.4.056.HW. My Notes

You may need to use the appropriate appendix table or technology to answer this question.

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 27 tires surveyed, the mean lifespan was 45,900 miles with a standard deviation of 9,700 miles. Using alpha = 0.05, is the data highly consistent with the claim?

State the null and alternative hypotheses (in miles). (Enter != for ≠ as needed.)

H₀:

H_a:

What is the test statistic? (Round your answer to two decimal places.)

What is/are the critical value(s)? (If using the z distribution round your answer(s) to two decimal places, and if using the t distribution round your answer(s) to three decimal places. Enter NONE for any unused answer blanks.)

lower tail upper tail

What is the decision of the test and what conclusions can be drawn?

At the 5% level of significance we would fail to reject H₀ and conclude that there is not sufficient evidence to conclude that the average life span of the tires is less than 50,000. At the 5% level of significance we would reject H₀ and conclude that there is not sufficient evidence to conclude that the average life span of the tires is less than 50,000. At the 5% level of significance we would fail to reject H₀ and conclude that there is sufficient evidence to conclude that the average life span of the tires is less than 50,000. At the 5% level of significance we would reject H₀ and conclude that there is sufficient evidence to conclude that the average life span of the tires is less than 50,000.

†

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8. 0/6 points | Previous Answers OSIntroBusStat1 11.2.077.HW. My Notes

You may need to use the appropriate technology to answer this question.

A plant manager is concerned her equipment may need recalibrating. It seems that the actual weight of the 15 oz. cereal boxes it fills has been fluctuating. The standard deviation should be at most 0.5 oz. In order to determine if the machine needs to be recalibrated, 88 randomly selected boxes of cereal from the next day's production were weighed. The standard deviation of the 88 boxes was 0.53. Does the machine need to be recalibrated? Conduct a hypothesis test at the 5% level.

State the null and alternative hypotheses. (Enter != for ≠ as needed.)

H₀:

H_a:

What is the test statistic? (Round your answer to three decimal places.)

What is/are the critical value(s)? (Round your answer(s) to three decimal places. Enter NONE for any unused answer blanks.)

lower tail

NONE

upper tail

What is the decision of the test and what conclusions can be drawn?

At the 5% level of significance we would fail to reject H₀ and conclude that, from the sample data, there is sufficient evidence to conclude that the machine needs to be recalibrated. At the 5% level of significance we would reject H₀ and conclude that, from the sample data, there is sufficient evidence to conclude that the machine needs to be recalibrated. At the 5% level of significance we would reject H₀ and conclude that, from the sample data, there is not sufficient evidence to conclude that the machine needs to be recalibrated. At the 5% level of significance we would fail to reject H₀ and conclude that, from the sample data, there is not sufficient evidence to conclude that the machine needs to be recalibrated.

†

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9. 0/3 points | Previous Answers OSIntroBusStat1 12.2.064.HW. My Notes

Three different traffic routes are tested for mean driving time. The entries in the table are the driving times in minutes on the three different routes. The one-way ANOVA results are shown in the table below.

Route 1	Route 2	Route 3
29	27	16
33	28	40
27	28	22
35	36	31

State

SS_between.

(Round your answer to one decimal place.)

29.2

State

SS_within.

(Round your answer to one decimal place.)

State the F statistic. (Round your answer to four decimal places.)

†

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WebAssign

Welcome, demo@demo

OpenStax - Intro to Business Statistics 1/e (Homework)

Current Score : 30 / 69

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving... ()

Instructions

Assignment Submission

Assignment Scoring

Part (a)

Part (b)

Part (c)

Part (d)

Part (e)

Part (f)

Part (a)

Part (b)

Part (c)

Part (d)

Part (e)

Part (f)