3. A producer of various kinds of batteries has been producing "D" size batteries with a lifeexpectancy of 87 hours. Due to an improved production process, management believes that therehas been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteriesshowed an average life of 88.5 hours. Assume from past information that it is known that thestandard deviation of the population is 9 hours.a. Give the null and the alternative hypotheses.b. Compute the test statistic.c. At 90% confidence using the critical value approach, test management's belief.d. At 99% confidence using the p-value approach, test management's belief.

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Answered: 3. A producer of various kinds of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A pizza delivery chain advertises that it will deliver your pizza in 2020 minutes from when the order is placed. Being a skeptic, you decide to test and see if the mean delivery time is actually more than 2020 minutes. For the simple random sample of 88 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 22.222.2 minutes with a standard deviation of 3.13.1 minutes. Assume that the population distribution is approximately normal. Perform a hypothesis test using a 0.0250.025 level of significance. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places. Step 3 of 3 : Draw a conclusion and interpret the decision.
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 31,000 miles and a standard deviation of 2400 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Tires that wear out by ? miles will be replaced free of charge.
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Some battery manufacturers claim that the average battery life of the company is 240 hours. There is a theory in the quality department of the company that the lifespan is different from 240 hours. The Quality Department therefore decided to conduct an experiment to test this theory. A random sample of size 18 was taken and the lifespan was examined. The average life of the batteries examined was 237,056 hours and the standard deviation was 11,280. Battery life can be expected to follow a normal distribution.a) Find a 95% confidence interval for the average battery life.b) Examine with an appropriate hypothesis test whether the average battery life differs from 240 hours.sometimes. Use α = 0.05.
1. The fuel efficiency of a new model pick-up truck (truck) is measured in miles per gallon (mpg). A company claims that their new truck gets 25 mpg on average. A consumer group thinks the company is lying and claims that the mean mileage for all the trucks is less than 25 mpg. In a random sample, of forty-five of these trucks the mean mpg was 23.3 mpg with a standard deviation of 5.1 mpg. a. Conduct a hypothesis test to test the consumer group's claim at the 5% significance level. Be sure to state you Ho and Ha, your test statistic and p- value, whether or not you reject Ho and whether you support the claim. b. Write a complete sentence describing what a Type I error is in context. c. Write a complete sentence describing what a Type II error is in context.
A pizza delivery chain advertises that it will deliver your pizza in 35 minutes from when the order is placed. Being a skeptic, you decide to test and see if the mean delivery time is actually more than 35 minutes. For the simple random sample of 14 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 37.0 minutes with a standard deviation of 9.9 minutes. Assume that the population distribution is approximately normal. Perform a hypothesis test using a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho: 35 Họ 1 = H₂H = 35
Suppose that an independent research company was tasked with testing the validity of complaints against a pesticide manufacturing firm for under-filling their 20 lb bags of pesticide. Past experience has shown that the amount of pesticide dispensed by the machines that fill the bags follows a normal distribution with a mean of 20 lb and a standard deviation of 0.6 lb. To verify the validity of the complaints, a researcher randomly selected 16 of the firm's 20 lb pesticide bags and recorded the following weights. 19.69, 19.5, 18.85, 18.56, 20.23, 20.3, 20.14, 19.11, 19.65, 18.87, 19.22, 19.24, 18.82, 20.23, 20.46, 18.66 If you wish, you may download the data in your preferred format. CrunchIt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc The mean weight of the 16 bags collected was 19.471 lb. Calculate the value of the one-sample z- statistic. Give your answer precise to three decimal places.
An article in the National Geographic News ("U.S. Racking Up Huge Sleep Debt." February 24, 2005) argues that Americans are increasingly skimping on their sleep A researcher in a small Midwestern town wants to estimate the mean weekday sleep time of its adult residents. He takes a random sample of 80 adult residents and records their weekday mean sleep time as 6.4 hours. Assume that the population standard deviation is fairly stable at 1.8 hours. [You may find it useful to reference the z table.) a. Calculate the 95% confidence interval for the population mean weekday sleep time of all adult residents of this Midwestem town (Round intermediote calculations to at least 4 decimal places. Round "z" volue to 2 decimol places and final answers to 2 decimal places.) Confidence interval to b. Can we conclude with 95% contfidence that the mean sleep time of all adult residents in this midwestern town is not 7 hours? O Yes, since the confidence interval contains the value 7 O Yes, since the…
(b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. • The value of the test statistic is given by √n The p-value is the area under the curve to the right of the value of the test statistic. O One-tailed o Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p- value. Step 4: Enter the p- value. (Round to 3 decimal places.) 0.3 0.2 0.1 (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the studio. o Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 90. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 90.…
Consumer agencies claim that the mean lifespan of a dishwasher is 9.5 years. Your company manufacturers dishwasher and you have been asked to see if this claim is true. You randomly survey 20 households who have recently purchased a dishwasher and ask them how long their previous dishwashers lasted and you calculate a mean of 8.9 years with a standard deviation of 3.1. Is the consumer agency’s claim that a dishwasher lasts 9.5 year correct? What is the p-value for this claim? Consumer agencies claim that the mean lifespan of a dishwasher is 9.5 years. Your company manufacturers dishwasher and you have been asked to see if this claim is true. You randomly survey 20 households who have recently purchased a dishwasher and ask them how long their previous dishwashers lasted and you calculate a mean of 8.9 years with a standard deviation of 3.1. Is the consumer agency’s claim that a dishwasher lasts 9.5 year correct? What is the p-value for this claim? 0.8012 0.1988 0.3975 -0.8656
2. The average gasoline price of one of the major oil companies has been $1.00 per gallon. Because of shortages in production of crude oil, it is believed that there has been a significant increase in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $1.04. Assume that the standard deviation of the population (o) is $0.12. a) State the null and the alternative hypotheses for testing the belief. b) Describe a Type I error and a Type II error for this situation. c) What is the critical value at a = .05? d) what's your What is the t-statistic or z-statistic associated with the above sample results?
Two species of fish have similar phenotvpes to each other, researchers wonder if they can classify these fish species based on their sizes. One species has mean size of 10cm, with standard deviation of 1. The other species has mean size of 12cm, with standard deviation of 2. Size of 15 fish from each species were measured. a. Which hypothesis testing method can be used to compare the mean size of the two populations? Perform the test for a = 0.01. How does result of this test help the researchers to decide if they can classify these fish species based on their sizes?

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