Intro Stats
4th Edition
ISBN: 9780321825278
Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 15, Problem 1E
Website An investment company is planning to upgrade the mobile access to their website, but they’d like to know the proportion of their customers who access it from their smartphones. They draw a random sample of 200 from customers who recently logged in and check their IP address. Suppose that the true proportion of smartphone users is 36%.
- a) What would you expect the shape of the sampling distribution for the sample proportion to be?
- b) What would be the
mean of this sampling distribution? - c) What would be the standard deviation of the sampling distribution?
a.
Expert Solution
To determine
Explain the shape of the sampling distribution for the sample proportion.
Answer to Problem 1E
The shape of the sampling distribution for the sample proportion is unimodal and symmetric.
Explanation of Solution
Given info:
A random sample of 200 is drawn from customers who recently logged in and checked their IP address and the smartphone users true proportion is 36%.
Justification:
Sampling distribution for a proportion:
For all possible samples the distribution of proportion is called the sampling distribution of proportion
- Samples should be independent.
- Sample size should be large.
- The sampling distribution of
Here random sample is drawn by considering 200 investors as a small portion of their customer. Therefore, the sampling distribution for the proportion of 200 investors that use smartphones would be unimodal and symmetrical.
b.
Expert Solution
To determine
Find the mean of this sampling distribution.
Answer to Problem 1E
The mean of this sampling distribution is 0.36.
Explanation of Solution
Justification:
From part (a), the mean for the sampling distribution of proportion is p.
Here, the true proportion smartphone users, is 36% that is, 0.36.
Thus, the mean of this sampling distribution is 0.36.
c.
Expert Solution
To determine
Find the standard deviation of the sampling distribution.
Answer to Problem 1E
The standard deviation of the sampling distribution is 0.034.
Explanation of Solution
Calculation:
From part (a), the standard deviation of
Here proportion p is 0.36 and q is
Substitute p as 0.36, q as 0.64 and n as 200 in the formula,
Thus, the standard deviation of the sampling distribution is 0.034.
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Example 4 (Part 2) We can use Statkey to take 50 different random samples of size 20 each, find the mean of
each sample, and compute a confidence interval for each one. The graph of the sampling distribution of the means
is on the left below, and that of the 50 confidence intervals is on the right.
1. What does each dot on the left hand dotplot represent?
StatKey Sampling Distribution for a Mean
Percent with Internet Access (Countries) ▾
Show Data Table Edit Data
Choose samples of size n =
20
Upload File
Change Column(s)
Generate 1 Sample
Generate 10 Samples
Generate 100 Samples
Generate 1000 Samples
Reset Plot
Sampling Dotplot of Mean
Left Tail Two-Tail Right Tail
60
50
40
40
30
20
20
10
samples = 50
mean = 41.626
std. error = 5.089
:
.:
:
::
0
25
30
35
40
45
50
55
60
41.626
Data Plots
Confidence Intervals
95%->
Confidence Intervals
Coverage
48/50 = 96%
20
40
60
80
2. Circle the confidence intervals that failed to capture the true mean.
3. Circle the sample means that produced those…
Example 4 (Part 1) One of the datasets in the Lock book
contains information about 215 countries of the world. One
of the variables is the percentage of people in the country
who have access to the internet. We have data for 203 of
those countries. The plot on the right shows a dotplot of
the data.
1. What are the cases?
Population
n = 203, mean = 43.024
median = 43.5, stdev = 29.259
20
2. What does each dot on the dotplot represent?
15
10
5
20
40
43.024
60
80
3. What type of data is do we collect from the cases, quantitative or categorical?
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n =6 professional basketball players gave the following information.
x
63
79
70
80
84
87
y
46
49
45
55
57
58
Find Se. Round your answer to three decimal places.
Chapter 15 Solutions
Intro Stats
Ch. 15.2 - You want to poll a random sample of 100 students...Ch. 15.2 - Prob. 2JCCh. 15.2 - If you think that about half the students are in...Ch. 15.5 - Prob. 4JCCh. 15.5 - Prob. 5JCCh. 15.5 - Prob. 6JCCh. 15.5 - Prob. 7JCCh. 15 - Website An investment company is planning to...Ch. 15 - Marketing The proportion of adult women in the...Ch. 15 - Prob. 3E
Ch. 15 - Character recognition An automatic character...Ch. 15 - Prob. 5ECh. 15 - Prob. 6ECh. 15 - Send more money The philanthropic organization in...Ch. 15 - Character recognition, again The automatic...Ch. 15 - Prob. 9ECh. 15 - Prob. 10ECh. 15 - Prob. 11ECh. 15 - Prob. 12ECh. 15 - Prob. 13ECh. 15 - Prob. 14ECh. 15 - Prob. 15ECh. 15 - Prob. 16ECh. 15 - Prob. 17ECh. 15 - Prob. 18ECh. 15 - 19. More coins Suppose the class in Exercise 17...Ch. 15 - 20. Bigger bag Suppose the class in Exercise 18...Ch. 15 - Prob. 21ECh. 15 - Prob. 22ECh. 15 - Prob. 23ECh. 15 - Prob. 24ECh. 15 - Prob. 25ECh. 15 - Prob. 26ECh. 15 - Prob. 27ECh. 15 - Prob. 28ECh. 15 - Prob. 29ECh. 15 - Prob. 30ECh. 15 - Prob. 31ECh. 15 - Prob. 32ECh. 15 - 33. Polling Just before a referendum on a school...Ch. 15 - Prob. 34ECh. 15 - Prob. 36ECh. 15 - Prob. 37ECh. 15 - 38. Meals A restaurateur anticipates serving about...Ch. 15 - Prob. 39ECh. 15 - Prob. 40ECh. 15 - Prob. 41ECh. 15 - CEO compensation The total compensation of the...Ch. 15 - Prob. 43ECh. 15 - Prob. 44ECh. 15 - GPAs A colleges data about the incoming freshmen...Ch. 15 - Prob. 46ECh. 15 - Lucky spot? A reporter working on a story about...Ch. 15 - Prob. 48ECh. 15 - Pregnancy Assume that the duration of human...Ch. 15 - Rainfall Statistics from Cornells Northeast...Ch. 15 - Prob. 51ECh. 15 - Prob. 52ECh. 15 - Prob. 53ECh. 15 - Prob. 54ECh. 15 - 55. AP Stats 2011 The College Board reported the...Ch. 15 - Prob. 56ECh. 15 - Prob. 57ECh. 15 - Prob. 58ECh. 15 - Prob. 59ECh. 15 - 60. Potato chips The weight of potato chips in a...Ch. 15 - Prob. 61ECh. 15 - 62. Milk Although most of us buy milk by the quart...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 1. Define probability: 2. Define statistics:arrow_forwardResults of tossing a coin four times: H, H, H, H How many times is the Coin expected to come up heads? How did you determine this number? Calculate the % deviation. Can these results be used to conclude that a coin is not fair? Why or why not?arrow_forwardCycles to failure Position in ascending order 0.5 f(x)) (x;) Problem 44 Marsha, a renowned cake scientist, is trying to determine how long different cakes can survive intense fork attacks before collapsing into crumbs. To simulate real-world cake consumption, she designs a test where cakes are subjected to repeated fork stabs and bites, mimicking the brutal reality of birthday parties. After rigorous testing, Marsha records 10 observations of how many stabs each cake endured before structural failure. Construct P-P plots for (a.) a normal distribution, (b.) a lognormal distribution, and (c.) a Weibull distribution (using the information included in the table below). Which distribution seems to be the best model for the cycles to failure for this material? Explain your answer in detail. Observation Empirical cumulative Probability distribution Cumulative distribution Inverse of cumulative distribution F-1 (-0.5) F(x)) (S) n 4 3 1 0.05 9 5 2 0.15 7 7 3 0.25 1 10 4 0.35 3 12 5 0.45 Normal…arrow_forward
- Problem 3 In their lab, engineer Daniel and Paulina are desperately trying to perfect time travel. But the problem is that their machine still struggles with power inconsistencies-sometimes generating too little energy, other times too much, causing unstable time jumps. To prevent catastrophic misjumps into the Jurassic era or the far future, they must calibrate the machine's power output. After extensive testing, they found that the time machine's power output follows a normal distribution, with an average energy level of 8.7 gigawatts and a standard deviation of 1.2 gigawatts. The Time Travel Safety Board has set strict guidelines: For a successful time jump, the machine's power must be between 8.5 and 9.5 gigawatts. What is the probability that a randomly selected time jump meets this precision requirement? Daniel suggests that adjusting the mean power output could improve time-travel accuracy. Can adjusting the mean reduce the number of dangerous misjumps? If yes, what should the…arrow_forwardProblem 5 ( Marybeth is also interested in the experiment from Problem 2 (associated with the enhancements for Captain America's shield), so she decides to start a detailed literature review on the subject. Among others, she found a paper where they used a 2"(4-1) fractional factorial design in the factors: (A) shield material, (B) throwing mechanism, (C) edge modification, and (D) handle adjustment. The experimental design used in the paper is shown in the table below. a. Run A B с D 1 (1) -1 -1 -1 1 2 a 1 -1 -1 1 3 bd -1 1 -1 1 4 abd 1 1 -1 1 5 cd -1 -1 1 -1 6 acd 1 -1 1 -1 7 bc -1 1 1 -1 abc 1 1 1 -1 paper? s) What was the generator used in the 2"(4-1) fractional factorial design described in the b. Based on the resolution of this design, what do you think about the generator used in the paper? Do you think it was a good choice, or would you have selected a different one? Explain your answer in detail.arrow_forwardSuppose we wish to test the hypothesis that women with a sister’s history of breast cancer are at higher risk of developing breast cancer themselves. Suppose we assume that the prevalence rate of breast cancer is 3% among 60- to 64-year-old U.S. women, whereas it is 5% among women with a sister history. We propose to interview 400 women 40 to 64 years of age with a sister history of the disease. What is the power of such a study assuming that the level of significance is 10%? I only need help writing the null and alternative hypotheses.arrow_forward
- 4.96 The breaking strengths for 1-foot-square samples of a particular synthetic fabric are approximately normally distributed with a mean of 2,250 pounds per square inch (psi) and a standard deviation of 10.2 psi. Find the probability of selecting a 1-foot-square sample of material at random that on testing would have a breaking strength in excess of 2,265 psi.4.97 Refer to Exercise 4.96. Suppose that a new synthetic fabric has been developed that may have a different mean breaking strength. A random sample of 15 1-foot sections is obtained, and each section is tested for breaking strength. If we assume that the population standard deviation for the new fabric is identical to that for the old fabric, describe the sampling distribution forybased on random samples of 15 1-foot sections of new fabricarrow_forwardUne Entreprise œuvrant dans le domaine du multividéo donne l'opportunité à ses programmeurs-analystes d'évaluer la performance des cadres supérieurs. Voici les résultats obtenues (sur une échelle de 10 à 50) où 50 représentent une excellente performance. 10 programmeurs furent sélectionnés au hazard pour évaluer deux cadres. Un rapport Excel est également fourni. Programmeurs Cadre A Cadre B 1 34 36 2 32 34 3 18 19 33 38 19 21 21 23 7 35 34 8 20 20 9 34 34 10 36 34 Test d'égalité des espérances: observations pairéesarrow_forwardA television news channel samples 25 gas stations from its local area and uses the results to estimate the average gas price for the state. What’s wrong with its margin of error?arrow_forward
- You’re fed up with keeping Fido locked inside, so you conduct a mail survey to find out people’s opinions on the new dog barking ordinance in a certain city. Of the 10,000 people who receive surveys, 1,000 respond, and only 80 are in favor of it. You calculate the margin of error to be 1.2 percent. Explain why this reported margin of error is misleading.arrow_forwardYou find out that the dietary scale you use each day is off by a factor of 2 ounces (over — at least that’s what you say!). The margin of error for your scale was plus or minus 0.5 ounces before you found this out. What’s the margin of error now?arrow_forwardSuppose that Sue and Bill each make a confidence interval out of the same data set, but Sue wants a confidence level of 80 percent compared to Bill’s 90 percent. How do their margins of error compare?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License