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Statistics, section 2, Fall 2019
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Peck - Statistics Companion 1/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 5 / 38

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

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

Ask Your Teacher Extension Requests Print Assignment

Question

Points

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Total

5/38 (13.2%)

Instructions

Statistics Companion: Support For Introductory Statistics by Roxy Peck and Tom Short, published by Cengage Learning, provides students with the support they need for developing statistical thinking and conceptual understanding of Statistics by diving into tactics for reading and understanding Statistics problems in context, supportive mathematics preparation, and study skills, and by fostering a productive mindset. Statistics Companion can be used with any Introductory Statistics textbook or resource. The WebAssign component for this text engages students with immediate feedback, an interactive eBook with online resources, question banks of end-of-section exercises, and a Midsemester Assessment to gauge student understanding of the foundational math skills covered in the first half of the textbook.

New for Spring 2021! Question 1 is an example of a Concept Video question (CV). Concept Video questions provide students with a Concept Video along with two to three comprehension questions. Concept Videos are 7-10 minutes in length and are designed to help students with big picture understanding of statistics.

New for Spring 2021! Question 2 contains a Master It tutorial (MI). Master It tutorials show students how to solve a similar problem in multiple steps by providing direction along with derivation, so the student understands the concepts and reasoning behind the problem solving.

Questions 3 through 5 provide scaffolding help for students as they are learning how to compute sample mean, sample variance, and sample standard deviation.

Questions 6 through 8 provide scaffolding help for students as they are learning how area under the normal distribution coincide with probability statements about random variables.

Question 9 estimates a population proportion and students answer questions about it.

Questions 10 through 12 provide scaffolding help for students as they are learning how to calculate margin of error, confidence intervals and how to interpret confidence intervals.

Questions 13 and14 provide scaffolding help for students learning the steps for hypothesis testing. 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.

The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

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. 2/3 points | Previous Answers PeckCoReq1 0.CE.001.CV. My Notes

2. 1/1 points | Previous Answers PeckCoReq1 1.3.039.MI. My Notes

Compare the numbers, and identify which is greater.

−522.2632 or −55.2732

The number

-55.2732

is greater.

Solution or Explanation

To help visualize the ordering of numbers for comparison, refer to the number line below and note that numbers to the left on the number line are less than the numbers to the right.

A number line that ranges from −10 to 10 is shown. The number line has tick marks:
−10,

−9,

−8,

−7,

−6,

−5,

−4,

−3,

−2,

−1,

0,

1,

2,

3,

4,

5,

6,

7,

8,

9,

and 10.

Begin by writing the numbers we are comparing, −522.2632 and −55.2732, so they have the same number of digits before and after the decimal place by adding 0s to the beginning or end of the number as needed.

first number −522.2632 second number −055.2732

To compare the numbers −522.2632 and −055.2732, examine the leftmost digits. In the first number, −522.2632, the leftmost digit is 5. In the second number, −055.2732, the leftmost digit is 0. Because these are negative numbers, the number with the smaller leftmost digit is the greater number.

The leftmost digit of the second number is smaller, so between the numbers −522.2632 and −55.2732 the number −55.2732 is greater.

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3. 2/3 points | Previous Answers PeckCoReq1 3.3.026. My Notes

For the data set, calculate

Σx, Σx², and (Σx)².

−8, −1, 3, 8, 1, 7, −7, 9, 6

Σx

Σx²

(Σx)²

324

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4. –/2 points PeckCoReq1 3.4.030.MI. My Notes

Calculate

and the sum of the squared deviations,

x − x

	2

(Round

to three decimal places and the sum of squared deviations to the nearest integer.)

−7, −1, 2, 7, 1, 4, −6, 9, 3

x − x

	2

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5. –/3 points PeckCoReq1 3.5.035.MI. My Notes

For the data set, calculate the sample mean

the sample variance,

s²,

and the sample standard deviation, s. (Round your answers to three decimal places.)

4, 7, 2, −2, −7

s²

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6. –/1 points PeckCoReq1 6.5.039. My Notes

Write the given statement using probability notation.

the probability that x takes a value between 8.6 and 8.8

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7. –/1 points PeckCoReq1 6.5.044. My Notes

Mark and shade the area represented by the given probability statement.

the probability that x takes a value between 100 and 600

A symmetric, bell-shaped curve is above a horizontal axis.

The horizontal axis has tick marks: −500, 0, 100, 500, 600, 1,000, 1,500, 2,000, and 2,500.

The curve enters the viewing window just above the axis at −500, reaches a peak at 1,000, and exits the viewing window just above the axis at 2,500.

The area under the curve, above the horizontal axis, and to the left of 100 is shaded. The area under the curve, above the horizontal axis, and to the right of 600 is also shaded.

A symmetric, bell-shaped curve is above a horizontal axis.

The horizontal axis has tick marks: −500, 0, 100, 500, 1,000, 1,500, 2,000, and 2,500.

The curve enters the viewing window just above the axis at −500, reaches a peak at 1,000, and exits the viewing window just above the axis at 2,500.

The area under the curve, above the horizontal axis, and to the right of 100 is shaded.

A symmetric, bell-shaped curve is above a horizontal axis.

The horizontal axis has tick marks: −500, 0, 500, 600, 1,000, 1,500, 2,000, and 2,500.

The curve enters the viewing window just above the axis at −500, reaches a peak at 1,000, and exits the viewing window just above the axis at 2,500.

The area under the curve, above the horizontal axis, and to the left of 600 is shaded.

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8. –/1 points PeckCoReq1 6.5.045. My Notes

For the shaded area given, write an appropriate probability statement in words and in symbols.

A symmetric, bell-shaped curve is above a horizontal axis.

The horizontal axis has tick marks: 10, 20, 30, 40, 50, 60, and 70.

The curve enters the viewing window just above the axis at 10, reaches a peak at 40, and exits the viewing window just above the axis at 70.

The area under the curve, above the horizontal axis, and between the approximate values 15 and 50 is shaded.

the probability that a variable x is less than 50: P(x < 50) the probability that a variable x is greater than 15: P(x > 15) the probability that a variable x is between 15 and 50: P(15 < x < 50) the probability that a variable x is not between 15 and 50: P(15 > x > 50) the probability that a variable x is between 10 and 50: P(10 < x < 50)

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9. –/8 points PeckCoReq1 8.1.001.MI. My Notes

Suppose that you want to estimate a population proportion and calculate a margin of error using data from a random sample. The sample size is

n = 76

and

p̂ = 0.42.

Check the necessary sample size condition, and comment on whether both parts are satisfied.

First we find np̂ = and n(1 − p̂) = . The quantity np̂ is 10, so this part of the condition satisfied. The quantity n(1 − p̂) is 10, so this part of the condition satisfied.

If the sample size condition is satisfied, then calculate the margin of error for a 95% confidence level. (Round your answer to three decimal places. If either part of the sample size condition is not satisfied enter NA.)

Interpret its value.

It is unlikely that the estimated proportion differs from the true population proportion by less than the value calculated above. It is impossible that the estimated proportion differs from the true population proportion by more than the value calculated above. It is likely that the estimated proportion differs from the true population proportion by the value calculated above. It is unlikely that the estimated proportion differs from the true population proportion by more than the value calculated above. The margin of error could not be estimated because at least one part of the sample size condition was not met.

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10. –/6 points PeckCoReq1 12.1.001.MI. My Notes

11. –/2 points PeckCoReq1 12.2.003. My Notes

Use the three-read strategy to understand the following exercise from a statistics textbook, and then proceed to complete the exercise.

An article describes a study of 218 business students at a large public university. Each student kept a log of time spent on various activities during a 1-week period. For these 218 students, the sample mean time spent studying was 9.67 hours and the sample standard deviation was 6.63 hours. Suppose that this sample was a random sample from the population of all business majors at this university and that you are interested in learning about the value of μ, the mean time spent studying for this population. Calculate the value of the margin of error (in hours). Use a 95% confidence level. (Round your answer to three decimal places.)

Interpret the margin of error in context.

The estimated mean never differs from the actual value of the population mean time spent studying by less than the value calculated above. It is unlikely that the estimated mean differs from the actual value of the population mean time spent studying by more than the value calculated above. There is a 95% chance that the estimated mean differs from the actual value of the population mean time spent studying by exactly the value calculated above. It is unlikely that the estimated mean differs from the actual value of the population mean time spent studying by less than the value calculated above. The estimated mean never differs from the actual value of the population mean time spent studying by more than the value calculated above.

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12. –/3 points PeckCoReq1 12.3.006. My Notes

Use the three-read strategy to understand the following exercise from a statistics textbook, and then proceed to complete the exercise.

Seventy-seven students at the University of Virginia were asked to keep a diary of a conversation with their mothers, recording any lies they told during this conversation.†Source: San Luis Obispo Telegram-Tribune, August 16, 1995 The mean number of lies per conversation was 0.5. Suppose that the standard deviation (which was not reported in the article) was 0.3, and that this group of 77 is representative of the population of students at this university. Construct a 95% confidence interval for the mean number of lies per conversation for this population. (Use the t critical value 1.992. Round your answers to three decimal places.)

Interpret the interval in context.

There is a 95% chance that the actual value of the population mean number of lies per conversation falls outside this interval. We can be 95% confident that the actual value of the population mean number of lies per conversation falls within this interval. There is a 95% chance that the actual value of the population mean number of lies per conversation falls within this interval. There is a 95% chance that the actual value of the population mean number of lies per conversation falls directly in the middle of this interval. We can be 95% confident that the actual value of the population mean number of lies per conversation falls directly in the middle of this interval.

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13. –/1 points PeckCoReq1 13.1.002. My Notes

A representative sample of size

n = 23

is selected from a population that is known to be normally distributed. The sample mean is

x = 7.6,

and the sample standard deviation is

s = 2.4.

Suppose that you want to test the null hypothesis

H₀: μ = 5.

Calculate the value of the test statistic. (Round your answer to three decimal places.)

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14. –/3 points PeckCoReq1 13.2.003.MI. My Notes

A study was conducted by researchers at a university who investigated whether time perception, an indication of a person's ability to concentrate, is impaired during nicotine withdrawal. After a 24-hour smoking abstinence,

n = 20

smokers were asked to estimate how much time had passed during a 45-second period. Suppose the resulting data on perceived elapsed time (in seconds) yielded a sample mean of

x = 58.8 seconds,

and sample standard deviation

s = 9.83 seconds.

Do the data from this study provide convincing evidence that the population mean estimated time is greater than 45 seconds? Use the three-read strategy to understand the problem, and then carry out a hypothesis test with a significance level of

α = 0.05.

State the appropriate null and alternative hypotheses.

Find the test statistic. (Round your answer to three decimal places.)

t =

If the P-value for this test is approximately 0, state the conclusion in the problem context.

Fail to reject H₀. There is convincing evidence that the population mean perceived elapsed time is greater than 45 seconds. Reject H₀. There is convincing evidence that the population mean perceived elapsed time is greater than 45 seconds. Reject H₀. There is not convincing evidence that the population mean perceived elapsed time is greater than 45 seconds. Fail to reject H₀. There is not convincing evidence that the population mean perceived elapsed time is greater than 45 seconds.

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