A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, μ, of 20 years. To test the company's claim, a competitor has selected 39 of these batteries at random. The mean lifetime of the sample is 21.1 years. Suppose the population standard deviation of these lifetimes is known to be 4.1 years. Is there enough evidence to reject the claim that the mean lifetime of the newest model is 20 years? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis and the alternative hypothesis H₁. Ho #:0 H D

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)

A chain of restaurants has historically had a mean wait time of 5 minutes for its customers. Recently, the restaurant added several very popular dishes back to their menu. Due to this, the manager suspects the wait time, μ, has increased. He takes a random sample of 35 customers. The mean wait time for the sample is 5.1 minutes. Assume the population standard deviation for the wait times is known to be 1.1 minutes. Can the manager conclude that the mean wait time is now greater than 5 minutes? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho: O H₁:0 μ X 0° OO 20ם ローロ OO × 5 (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test. 0.10 is the value that cuts off an area of 0.10 in the right tail. *-μ ⚫ The test statistic has a normal distribution and the value is given by z=- σ √n Standard Normal…

A manufacturer of TV tubes has for many years used a process giving a meantube life of 4700 hours and a standard deviation of 1460 hours. A new process is tried to see if it will increase the life significantly. A sample of 100new tubes gave a mean life of 5000 hours. Is the new process better than the old one at a 1% level of significance?

The length of students' college careers at Anytown University is known to be normally distributed, with a mean length of 5.5 years and a standard deviation of 1.75 years. What is the lower quartile for the length of students' careers at Anytown University?

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…

The manufacturer of a particular brand of tires claims they average at least 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles. A survey of tire owners was conducted. From the 21 tires surveyed, the mean lifespan was 41500 miles. Using alpha = 0.05, can we prove that the data in inconsistent with the manufacturers claim? What is the Test Statistic

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 62 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 58 and 62?ans =  %

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.9 years, and standard deviation of 1.6 years.The 2% of items with the shortest lifespan will last less than how many years?