A company that makes batteries for electric cars indicates that its newest model of battery has an average life,µ,of25years. To prove the company's claim, acompetitor has selected61of these batteries randomly. The average duration of the show is26.1years. Suppose the population standard deviation of thesedurations is known to be4.5 years.Is there sufficient evidence to reject the claim that the median lifetime of the newer model is25years? Perform a hypothesis test using the significance level of0.10.(a) Formulate the null hypothesish and the alternative hypothesish 1'ho:h₁:01:(b) take a testz and find the p-value.This information will help you perform the testz.• The value of the test statistic is given by#112²noμO ●Hep-valueis twice the area under the curve to the right of the value of the test statistic.standard normal distributionStep 1: Select one queue or twoqueues.A tailtwo tailsStep 2: Enter the test statistic.(Round to 3 decimal places.Step 3: Shade the area represented bythe p value.Step 4: Enter the p- value.(Round to 3 decimal places.2- 10.40.30.2 +0.1+ta23

The question is about hypothesis testing.Given :Population mean life of a newest model of battery (…

Answered: A company that makes batteries for…

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

Similar questions

A sample of 10 from population 1 has a mean of 32 and a standard deviation of 6. A sample of 13 from population 2 has a mean of 48 and a standard deviation of 8. The population standard deviations are unknown but assumed to be equal. Test the hypothesis, at the 1% level of significance, that the population means are the same. State your conclusion as a sentence and include the test statistic and the critical value.
An engineer working for a tire manufacturer investigates the average life of a new material to be used in the manufacturing process. For this purpose, he builds a sample of 13 tires and tests them in a laboratory until the end of their useful life is reached. The data obtained from the sample are as follows: average of 60897.9 km and standard deviation of 2734.8 km. The engineer would like to demonstrate that the average service life of the tire with the new material exceeds 60,000 km. a) State the null and alternative hypothesis to be stated in this experiment. Test the stated hypotheses using an α = 0.05 What conclusions are reached? b) Find a 95% confidence interval for the average tire life with the new material. Interpret your answer. (RESPOND MANUALLY) (RESPOND MANUALLY)
In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?
A fiber spinning process currently produces a fiber whose strength is normally distributed with a mean of 75 Pa. The minimum acceptable strength is 65Pa. If 10% of the fiber produced by the current method fails to meet the minimum specifications, what is the standard deviation of fiber strengths in the process? If the mean remains at 75 Pa, what must the standard deviation be so that only 1% of the fiber will fail to meet the specifications? Given that the standard deviation is 5Pa, to what value must be mean be set so that only 1% of the fiber will fail to meet the specifications?
Currently patrons at the library speak at an average of 61 decibels. Will this average increase after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 57 people speaking at the library. Their average decibel level was 63.8 and their standard deviation was 9. What can be concluded at the the αα = 0.10 level of significance?
According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 49 months. A researcher for a consumer advocate group ests this by selecting 70 bulbs at random. For the bulbs in the sample, the mean lifetime is 46 months. It is known that the population standard deviation of he lifetimes is 9 months. Can we conclude, at the 0.01 level of significance, that the population mean lifetime, μ, of light bulbs made by this manufacturer differs from 49 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H₁. Ho :D H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.)…
A manufacturer claims that the mean lifetime, u, of its light bulbs is 44 months. The standard deviation of these lifetimes is 7 months. Twenty-three bulbs are selected at random, and their mean lifetime is found to be 48 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 44 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) v O=0 OSO |(c) Find the value of the test statistic. (Round to three or more decimal places.) O
A study of B.A. (Hons.) Economics examination results of 1000 students in 1990 gave the mean теаn grade as 78 and the standard deviation as 8.0. A similar study in 1995 revealed the mean grade of the group as 80 and the standard deviation as 7-6. In which year was there the greater (i) absolute dispersion, (ii) relative dispersion ? What can we say about the average performance of the students over time?
A manufacturer claims that the mean lifetime, u, of its light bulbs is 42 months. The standard deviation of these lifetimes is 6 months. Twenty-seven bulbs are selected at random, and their mean lifetime is found to be 41 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 42 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H1. p H, :0 H, :0 (b) Determine the type of test statistic to use. D=D OSO (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or more decimal places.) Dand (e) Can we conclude that the mean lifetime of…
The manufacturer of Suzanne Space Saver tables finds that the mean time needed by online buyers to assemble the tables is 1 hour with a standard deviation of 0.25 hours. The design team of the firm has developed a new manual to reduce the time needed to assemble the table by its buyers. To test the effectiveness of the new manual, the team selects and gives 20 buyers the new manual to use. The sampled buyers take a mean of 0.45 hours to assemble each table. Assuming that the population is normally distributed, and using the 0.05 level of significance, determine and interpret the p value for the test and state whether we should conclude that the new manual is effective.
A large manufacturing plant uses lightbulbs with lifetimes that are normally distributed with a mean of 1500 hours and a standard deviation of 80 hours. To minimize the number of bulbs that burn out during operating hours, all bulbs are replaced at once. How often should the bulbs be replaced so that only 1% burn out between replacement periods? (Round your answer to one decimal place.)
A manufacturer claims that the mean lifetime, μ , of its light bulbs is 55 months. The standard deviation of these lifetimes is 6 months. Forty-two bulbs are selected at random, and their mean lifetime is found to be 58 months. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 55 months? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.) The two critical values at the 0.05 level of significance:(Round to at least three decimal places.) and Can we…

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS