The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 427 consumers who have owned a ColorSmart-5000 television set for five years. Of these 427 consumers, 314 say their ColorSmart-5000 television sets did not need a repair, whereas 113 say their ColorSmart-5000 television sets did need at least one repair. (a) Find a 99 percent confidence interval for the proportion of all ColorSmart-5000 television sets that have lasted at least five years without needing a single repair. (Round your answers to 3 decimal places.) The 99 percent confidence interval is (b) Does this confidence interval provide strong evidence that the percentage of all ColorSmart-5000 television sets that last at least five years without a single repair is less than the 95 percent claimed by the manufacturer? the interval is 0.95.

The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 427 consumers who have owned a ColorSmart-5000 television set for five years. Of these 427 consumers, 314 say their ColorSmart-5000 television sets did not need a repair, whereas 113 say their ColorSmart-5000 television sets did need at least one repair. (a) Find a 99 percent confidence interval for the proportion of all ColorSmart-5000 television sets that have lasted at least five years without needing a single repair. (Round your answers to 3 decimal places.) The 99 percent confidence interval is (b) Does this confidence interval provide strong evidence that the percentage of all ColorSmart-5000 television sets that last at least five years without a single repair is less than the 95 percent claimed by the manufacturer? the interval is 0.95.

Name: The manufacturer of the ColorSmart-5000 television set claims 95 perc
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a singlerepair. In order to test this claim, a consumer group randomly selects 427 consumers who have owned a ColorSmart-50

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: In a survey of 163 subjects, each was asked to indicate how many text messages they send and receive…

A: problem is solved { if it helps please leave positive rating it's matter alot to us Thank you…

Q: hypothesis H0:p=0.65 where p is the proportion of all adults in the city who meet or exceed the…

A: Given that n=400 , X=245 , p0=65%=0.65 p=X/n

Q: The research group asked the following question of individuals who earned in excess of $100,000 per…

Q: Sally is interested in finding out if the political party affiliation of Americans who are…

Q: 5000 teleVision se ercent Tive years thout hee repair. In order to test this claim, a consumer group…

A: The value of z at a 99% confidence level is 2.576, which can be obtained by using the standard…

Q: 2. An educational psychologist is interested in whether using a child's own name in a story affected…

A: Given information: Student Ordinary story Own Name story A 2.00 G 7 B 3.00 H 10 C…

Q: An anger-management course claims that, after completing its seminar, participants will lose their…

A: (1)

Q: Joe's electric company made 17 customer calls last week and 23 calls this week. How many calls must…

Q: A mayor running for re-election claims that during his term, average municipal taxes have fallen by…

A: Probability : Probability is a field of mathematics that deals with numerical descriptions of how…

Q: In a survey of 380 households regarding the ownership of HD TVs and non-HD TVs, the following data…

A: Let us denote:H=event of having one or more HD TVsN=event of having one or more non-HD TVsGiven that…

Q: Gallup conducted a survey of 1,015 randomly selected U.S. adults about "Black Friday" shopping. They…

Q: An anger-management course claims that, after completing its seminar, participants will lose their…

Q: Researchers conducted a study to find out if there is a difference in the use of online-learning by…

A: State the appropriate hypothesis: Let p1 be the population proportion of online learning by 16-29…

Q: rding to a recent census, 15% of the people in the United States are of Hispanic origin. One county…

A: given data n = 457 x = 48 claim = p ≠ 0.15

Q: A survey of 125125 freshmen business students at a local university produced the results listed…

Q: Fil in the missing values in the contingency table. Round your expected frequencies to two or more…

A: As pr our guidelines, we are allowed to answer first three sub-parts only. Thanks Given Frequency…

Q: True or false? Less than 25 percent of Thursdays had a higher number of hits than the busiest…

A: The boxplots show the number of hits at a certain website for the different days of the week.

Q: A mayor running for re-election claims that during his term, average municipal taxes have fallen by…

A: Null Hypothesis is a neutral statement about the parameter or distribution. Alternative hypothesis…

Q: A mayor running for re-election claims that during his term, average municipal taxes have fallen by…

A: The population standard deviation is 35.

Q: According to the most recent data, 9.5% of engineers (electrical, mechanical, civil, and industrial)…

A: Population proportion is p=0.095 . Sample size is n=75 .

Q: A mayor running for re-election claims that during his term, average municipal taxes have fallen by…

A: Given that The hypothesis is

Q: A survey of 800 nurses yielded the following information: 430 were health club members, 555 were…

A: Given data, Total number of nurses=800 in which Health club member nurses =430 Smokers nurses =555…

Q: A mayor running for re-election claims that during his term, average municipal taxes have fallen by…

Q: Residents in a city are charged for water usage every three months. The water bill is computed from…

A: INTRODUCTION : HISTOGRAM: The Histogram is often useful to represent a frequency distribution…

Q: A mayor running for re-election claims that during his term, average municipal taxes have fallen by…

Q: A research wants to determine if pre-natal exposure to the hormones in birth control pills alters…

A: The researcher exposes a group of pregnant midshipman fish to birth control hormones and records the…

Q: In a survey of 1000 randomly selected adults in the United States, participants were asked what…

A: We need to find confidence intervals.

Q: In March 2017, 9,195 men took trips with median duration of 300 seconds, and 2,439 women took…

A: The median duration of trips for 9195 men is 300 seconds and the median duration for 2439 women is…

Q: A mayor running for re-election claims that during his term, average municipal taxes have fallen by…

A: Given data…

Concept explainers

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

Topic Video

Question

The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a single
repair. In order to test this claim, a consumer group randomly selects 427 consumers who have owned a ColorSmart-5000 television
set for five years. Of these 427 consumers, 314 say their ColorSmart-5000 television sets did not need a repair, whereas 113 say their
ColorSmart-5000 television sets did need at least one repair.
(a) Find a 99 percent confidence interval for the proportion of all ColorSmart-5000 television sets that have lasted at least five years
without needing a single repair. (Round your answers to 3 decimal places.)
The 99 percent confidence interval is
(b) Does this confidence interval provide strong evidence that the percentage of all ColorSmart-5000 television sets that last at least
five years without a single repair is less than the 95 percent claimed by the manufacturer?
the interval is
0.95.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Given

VIEW

Solution (a)

VIEW

Solution (b)

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Data Collection, Sampling Methods, and Bias$

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

A mayor running for re-election claims that during his term, average municipal taxes have fallen by $100. A conscientious statistician wants to test this claim. He surveys 38 of his neighbors and finds that their taxes decreased (in dollars) as follows:113, 85, 109, 97, 117, 87, 105, 116, 84, 122, 118, 107, 108, 115, 100, 100, 107, 111, 101, 108, 71, 107, 80, 103, 86, 121, 117, 83, 113, 107, 124, 102, 78, 112, 96, 97, 88, 117The statistician assumes a population standard deviation of $14. Do you think the statistician should reject the mayor's claim? Why or why not?Step 1: State the hypothesis. = Step 2: Determine the Features of the Distribution of Point Estimates Using the Central Limit Theorem.By the Central Limit Theorem, we know that the point estimates are ___ with distribution mean ____ and distribution standard deviation ______.Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate.P(___ ___ ___ ) = P(___ ___ _____ )= _____
A statistics instructor would like to know whether it is worthwhile to require students to do weekly homework assignments. For Section1 of the course, homework is assigned, collected and graded each week. In Section2, students are not required to turn in homework. At the end of the semester, the students are given the same final exam. In Section1, the numbers of students getting each grade are: 16 students got A, 22 students got B, 8 students got C, and 4 students got D. In Section2, the numbers of students getting each grade are: 8 students got A, 18 students got B, 18 students got C, and 6 students got D. Is there an association between assigning homework and exam grade? Test at the alpha = 0.05 level. a. We reject the null hypothesis with two-tailed critical values; there is an association between assigning homework and exam grade. b. We reject the null hypothesis with one-tailed critical value; there is an association between assigning homework and exam…
In a memory test, the test subjects are given a large number and are asked to memorize it. Historical records show that 80% of test subjects pass the test. To pass the test, a subject must exactly repeat all the digits in the number after two hours. A random sample of 625 people to take the memory test is going to be chosen. Let p be the proportion of people in the sample who pass the test. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of P. 0 (b) Find the standard deviation of p. 0 (c) Compute an approximation for P(P >0.84), which is the probability that more than 84% of the people in the sample pass the test. Round your answer to four decimal places. 0 X
A mayor running for re-election claims that during his term, average municipal taxes have fallen by $125. A conscientious statistician wants to test this claim. He surveys 37 of his neighbors and finds that their taxes decreased (in dollars) as follows: 121, 139, 121, 125, 118, 145, 141, 91, 127, 136, 144, 154, 131, 139, 139, 125, 108, 130, 125, 106, 137, 148, 154, 134, 137, 112, 96, 114, 114, 126, 133, 129, 94, 129, 148, 163, 121 The statistician assumes a population standard deviation of $19. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. ?v= Step 2: Determine the Features of the Distribution of Point Estimates Using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are [Select an answer with distribution mean and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P? ✓ ? ♥ = P(? ? ♥
A report describes a survey of 251 adult Americans. Participants in the survey were asked how often they disinfect their phone and were asked to respond with one of the following categories: more than once a week, once a week, every other, week, every three weeks, or less often than every three weeks. For this group, 9% responded more than once a week, 52% responded once a week, 26% responded every other week, 6% responded every three weeks, and 7% responded less often than every three weeks. Fill in the table below with the relative frequency distributions. How Often? Relative Frequency More than once a week Once a week Every other week Every three weeks Less often than every three weeks
The owner of a dry cleaning business studied the number of dry-cleaned items that were returned for rework per day for a 4-week period (Mon-Sat). The results are given below. Complete (a) through (c). Time Items Returned Items Returned 1 6 Time 13 Items Returned 10 4 16- 2 10 12 Time AMANY 3 4 14 15 16 17 5 10 6 4 5 가더 24 5 9 6 10 18 9 7 5 19 20 10 10 a. Construct a c chart for the items per day that are returned for rework. Do you think that the process is in a state of statistical control? Choose the correct chart below. O A. O Items Returned B. 8 6 16- 0 9 8 21 5 Full data set 10 11 12 6 5 7 22 23 24 9 9 12 12 Time ² 24 O C. Items Returned 16- wwwww 12 Time 24
Suppose you are the manager of two beachfront hotels : The Palms and Golden Sands. You'd like to know if there is a difference in guest satisfaction between the two hotels. To investigate this, you conduct a survey and ask guests upon departure if they are likely to return to the hotel in the future. For The Palms, 163 out of 227 guests who were surveyed responded " yes ". For Golden Sands, 154 out of 262 guests responded "yes ". Answer the following questions. Round any numbers in your final answers to 2 decimals. 1) Calculate a 95 % confidence interval for the difference in satisfaction rates between The Palms and Golden Sands (Show work) 2) Use the critical value approach to test, at a 1% significance level, whether or not the guest satisfaction rates are different between the two hotels. What do you conclude ? (In your answer, show the steps involved with testing) 3) What is the p-value of your test in part 2?
A mayor running for re-election claims that during his term, average municipal taxes have fallen by $150. A conscientious statistician wants to test this claim. She surveys 45 of her neighbors and finds that their taxes decreased (in dollars) as follows: 149, 135, 147, 147, 160, 146, 165, 144, 142, 159, 138, 185, 143, 164, 143, 154, 163, 151, 171, 156, 133, 145, 180, 172, 166, 167, 149, 144, 154, 172, 138, 168, 179, 151, 131, 165, 114, 140, 162, 151, 136, 152, 157, 154, 136 The statistician assumes a population standard deviation of $13. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. ? Step 2: Determine the Features of the Distribution of Point Estimates Using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are [Select an answer distribution mean with and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P? ✓ ? ✓…
In a series of studies, Sebastian Deri and his colleagues (2017) asked multiple groups about the number of friend groups they had and how often they attended different social events. They then asked participants how they thought their own numbers compared to other people's: Did participants see themselves as less social, the same as, or more social than others? In the first study, the researchers reported that: "Three hundred four participants from Amazon's Mechanical Turk (150 women; Mage = 37.1; 78% White, 10% Black, and 6% Asian) completed a survey in exchange for modest payment" (p. 860). What do the researchers mean by "Amazon's Mechanical Turk" with respect to their sample of participants? O A. An archival data set that already exists and from which researchers can use data O B. An online tool that researchers can use to recruit people to participate in research in exchange for a small payment O C. An e-book sold by Amazon that includes contact information for possible…
A report described teens' attitudes about traditional media, such as TV, movies, and newspapers. In a representative sample of American teenage girls, 42% said newspapers were boring. In a representative sample of American teenage boys, 45% said newspapers were boring. Sample sizes were not given in the report. A button hyperlink to the SALT program that reads: Use SALT. (a) Suppose that the percentages reported had been based on a sample of 50 girls and 40 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using ? = 0.05. (Use pgirls − pboys.) Find the test statistic. (Round your answer to two decimal places.) z = Find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Reject H0. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who…