A manufacturer of flashlight batteries claims that the average life of her batteries islarger than 400 hours. Peter, as a quality assurance officer in the manufacturingcompany, took a random sample of 13 batteries from a day's production andused them continuously until they failed to work. The lifetime (hours) until failure was:3424263175452644511049631512266492562298(a) At the 0.05 level of significance, is there evidence that the manufacturer's claim iscorrect?(b) What is the p-value?

Given data is342,426,317,545,264,451,1049,631,512,266,492,562,298Mean(x)=sum of the data settotal…

Answered: A manufacturer of flashlight batteries…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.38. Suppose a random sample of 105 traffic fatalities in a certain region results in 51 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the a = 0.01 level of significance? Because npo (1 - Po 10, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis satisfied. (Round to one decimal place as needed.) can be reasonably assumed to be random, What are the null and alternative hypotheses? is given to be random, cannot be reasonably assumed to be random, Ho: versus H,: (Type integers or decimals. Do not round.) is given to not be random, Find the test statistic, zo. Z0 = (Round to two decimal places as needed.) Find the P-value.…
The General Social Survey (GSS) collects data on demographics, eduction and work, among many other characteristics of US residents. Suppose we want to estimate the difference between the average number of hours worked by all Americans with a college degree and those without a college degree. Is there sufficient evidence that there is a significant difference between the average number of hours worked by those Americans with a college degree vs. those Americans without a college degree? Use the following output: Welch Two Sample t-testdata: yes and not = 3.1181, df = 1098.5, p-value = 0.001867alternative hypothesis: true difference in means is not equal to 095 percent confidence interval: 1.011652 4.445822sample estimates:mean of x mean of y 42.81574 40.08701 Using the provided output, find the 95% confidence interval for the difference of the average amount of hours worked for those that have a college degree vs. those that do not have a college degree (ie: for the difference of two…
A scientist selected a random sample of seven varieties of peach ice cream to investigate the relationship between the density, in pounds per cubic inch, of the varieties of ice cream and the percent concentration of peaches in the ice cream. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence at the 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream? A A two-sample t-test for a difference between means B C D E A chi-square test of independence A linear regression t-test for slope A two-sample z-test for a difference between proportions A matched pairs t-test for a mean difference S
he data on the number of chocolate chips per bag for 42 bags of Chips Ahoy! cookies were obtained by the students in an introductory statistics class at the United States Air Force Academy in response to the Chips Ahoy! 1,000 Chips Challenge sponsored by Nabisco, the makers of Chips Ahoy! Use the data collected by the students to answer the following questions and to conduct the analyses required in each part. They found ¯xx¯ = 1261.6 and s = 117.6 a. Determine a 95% confidence interval for the mean number of chips per bag for all bags of Chips Ahoy! cookies. ≤μ≤≤μ≤ b. Interpret your result in words. c. Can you conclude that the average bag of Chips Ahoy! Cookies contain at least 1000 chocolate chips? yes no
Concerned about the initial monitoring data, the environmental action group decides to continue to monitor the plant, and try to gather more evidence for their case. A random sample of twenty-six hours is selected over a period of a week. The observations (gallons of wastewater discharged per hour) are 1036 1047 996 1052 1136 1131 958 1058 1087 1146 1111 1040 884 997 1130 994 963 1127 1136 1126 The output of a statistical analysis software on this dataset is shown below N Mean Std. Dev. 26 1081 89.6 Reading the output, we find that • The sample size is n = • The sample mean is a • The sample standard deviation is s = • From this we can calculate the standard error to be SE Note that the observed sample mean is is greater than 1000 gallons per hour. This could mean that the plant is discharging more wastewater than they promised, or the plant could be in compliance, and the large numbers were due to sampling variability. To see if this is the case, we will test the hypothesis that u…
The amount of sodium (in milligrams) in one serving for a random sample of three different kinds of foods is listed. Find the critical value for testing for a difference in the mean sodium amounts at the a = 0.05 level of significance. Condiments Cereals 180 160 230 200 220 190 140 300 250 240 220 160 150 310 A) 3.05 B) 3.47 C) 0.33 D) 3.52 Desserts 340 130 280 230 210 150 340 120
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A cell phone manufacturer tests the battery lifetimes of its cell phones by recording the time it takes for the battery charges to run out while testers are streaming videos on the phones continuously. The manufacturer claims that the population mean of the battery lifetimes of all phones of their latest model is 5.26 hours. As a researcher for a consumer information service, you want to test that claim. To do so, you select a random sample of 45 cell phones of the Español manufacturer's latest model and record their battery lifetimes. Assume it is known that the population standard deviation of the battery lifetimes for that cell phone model is 2.42 hours. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. Then state whether the confidence interval you construct contradicts the manufacturer's claim. (If necessary, consult a list of formulas.) 00 (a)…
How long it takes paint to dry can have an impact on the production capacity of a business. An auto body & paint business invested in a paint-drying robot to speed up its process. An interesting question is, "Do all paint-drying robots have the same drying time?" To test this, suppose we sample five drying times for each of different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Suppose the following data were obtained. Robot 4 Robot 1 128 138 134 125 135 Robot 2 143 134 142 147 | Ho: M₁ = 1₂ = 13 = 14 H₂: M₁ # M₂ # Hz # H4 124 4ܐ = 3ܬܐ = 2ܬܐ = 1ܐ :Ha Robot 3 132 142 | Ho: M₁ # M₂ # M3 # H4 H₂: M₁ = 1₂ = 13 = 14 138 135 128 ⒸH₁: M₁ = H₂ = 143 = 14 H: Not all the population means are equal. 151 142 At the α = 0.05 level of significance, test to see whether the mean drying time is the same for each type of robot. State the null and alternative hypotheses. O Ho: Not all the population means are equal. 136…
The Substance Abuse and Mental Health Services Administration (SAMHSA, 2017) estimates that 10.9% of the population of the United States age 18–24 had an episode of depression in the previous 12 months. Suppose a researcher takes a random sample of 225 United States adults aged 18–24. Determine the value of the sample proportion, p, such that 5% of samples of 225 United States adults age 18–24 are greater than p. You may find software or a z-table useful. Give your answer precise to three decimal places. p = II
Dr. Maddan's eye drops are supposed to cause significant reduction is eye redness. The following table shows the results of a recent study where a random sample of individuals took part in a placebo controlled study. No Reduction in Redness Reduction in Redness Total Eye Drops 120 220 340 No Eye Drops Total 120 140 260 240 360 600 With 5% level of significance, determine if eye redness reduction is dependent upon taking the eye drops. Provide, a. the Chi-square statistic. b. the critical value or the p-value. c. Your decision on whether or not to reject Ho.
Clothes dried outside smell better than those dried in a dryer because of a process called photolysis. Sunlight breaks down compounds that cause odor. A trained smeller is asked to smell a random sample of 20 towels. The smeller does not know it, but all of the 20 towels have been dried in the sun. The smeller is blindfolded and is not allowed to touch the towels but leans forward to smell the towel then rates the towel on a smell-scale of 1 to 10, where 1 is the an extremely unpleasant smell and 10 is a very good smell. A smell rating of 8 is typically attributed to a towel that is dried in the dryer. The mean smell rating for these 20 towels is approximately normal with a mean of 8.45 and the standard deviation is 0.887. A statistician performs a test of Ho μ = 8 versus H₁ μ> 8 where is the true mean smell rating for all towels dried in the sun. This test yields a P-value of 0.0176. What conclusion would you make at the significance level a = 0.05? Because the P-value of 0.0176 < α =…

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