A manufacturer of sports equipment has developed a new synthetic fishing line that claims to have a mean breaking strength of 10kg with a standard deviation of 0.7kg. Test the hypothesis that p = 10kg against p # 10kg and find if a random sample of 55 lines is tested and found to have mean breaking strength of 8kg. Use 0.01 level of significance.
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- According to a leasing firm's reports, the mean number of miles driven annually in its leased cars is miles with a standard deviation of miles. The company recently starting using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean number of miles driven annually under the new contracts, , is less than miles. He takes a random sample of cars under the new contracts. The cars in the sample had a mean of annual miles driven. Assume that the population is normally distributed. Is there support for the claim, at the level of significance, that the population mean number of miles driven annually by cars under the new contracts, is less than miles? Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts. Perform a one-tailed test. Then answer the questions below.Carry your intermediate computations to three or more decimal places, and round your responses…poll used a sample of 100 randomly selected car owners. Within the sample, the mean time of ownership for a single car was 7.18 years with a standard deviation of 3.37 years. Test the claim by the owner of a large dealership that the mean time of ownership for all cars is less than 7.5 years. Use a 0.05 significance level. Find the Z score and P value and if left-tailed or right-tailed. Also to reject or not too.The Sunny Dale Bank monitors the time required to serve customers at the drive-through window because it is an important quality factor in competing with other banks in the city. After analyzing the data gathered in an extensive study of the window operation, bank management determined that the mean time to process a customer at the peak demand period is 5 minutes, with a standard deviation of 1.5 minutes. Management wants to monitor the mean time to process a customer by periodically using a sample size of six customers. Assume that the process variability is in statistical control. Design an x-chart that has a type I error of 5 percent. That is, set the control limits so that there is a 2.5 percent chance a sample result will fall below the LCL and a 2.5 percent chance that a sample result will fall above the UCL. After several weeks of sampling, two successive samples came in at 3.70 and 3.68 minutes, respectively. Is the customer service process in statistical control?
- A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 6,192 with a standard deviation of 699. Of the 35 two-year colleges surveyed, the mean enrollment was 4,354 with a standard deviation of 781. Test the student's claim at the 0.1 significance level. Determine the test statistic. Round to four decimal places.t=_________ Find the pp-value. Round to 4 decimals.p-value = _________A computer software vendor claims that a new version of its operating system will crash fewer than six times per year on average. A system administrator installs the operating system and claims that the new operating system will crash more than six times per year on average. At the end of year, the system administrator samples 41 computers with the new operating system and finds that the mean number of crashes on those computers for the year was 7.1 with sample standard deviation of 3.6 crashes. Can you conclude that the system administrator’s claim is correct? Use the critical value method to perform a hypothesis test at the 0.05 level of significance. a. Define the parameter we are testing and setup a hypothesis test to test the administrator’s claim: b. Calculate the test statistics for this hypothesis test. c. What is the critical value for this hypothesis test?A sample of 45 adult men from Lahug showed that the mean time they spend working from home is 28.50 hours per week with a standard deviation of 4 hours. Another sample of 40 adult men from Pardo showed that the mean time spent by them working from home is 23.25 hours per week with a standard deviation of 5 hours. Using a 2.5% significance level, can you conclude that the mean time spent working from home by adult men in Lahug is greater than that for adult men in Pardo? Assume that the standard deviations for the two populations are equal.
- A cold medicine lists 600 milligrams of acetaminophen per fluid ounce as an active ingredient. A test of 75 one-ounce samples of the medicine finds that the mean amount of acetaminophen for the sample is 598 milligrams with a standard deviation of 20 milligrams. Test the claim that the medicine does not contain the required amount of acetaminophen. Use a 0.05 significance level. State the null and alternative hypotheses. O A. Ho: μ = 600 milligrams H₂:μ>600 milligrams OC. Ho: μ = 600 milligrams H₂: μ< 600 milligrams Find the z-score. Z= (Round to two decimal places as needed.) B. Ho: μ = 600 milligrams H₂: μ#600 milligrams O D. Ho: μ#600 milligrams H₂: μ = 600 milligrams M-IThe BDHS reported that the mean cholesterol level in 2020 for all adults was 203 in a certain area. Around a sample of 3,310 participants were questioned about the cholesterol levels who attended the last month survey and it is found that mean cholesterol level is 200.3 with a standard deviation of 36.8. Is there any statistical evidence of a difference in mean cholesterol levels in that area? Conduct the test at 1% level of significance. a. Which of the following statistical tests is most appropriate in this scenario? Two-Tailed Z-Test One-Tailed Z-Test Two-Tailed T-Test One-Tailed T-Test b. What are the appropriate hypotheses for the test? Но : д — 203 Н : д + 203 Но : д + 203 Н] :д — 203 Но : и — 200.3 Ні : д > 200.3 Ho : µ = 200.3 H1 : µ < 200.3 C. After conducting the appropriate significance test, the test statistic was found to be -4.22. Therefore, the conclusion for the test is: Reject Ho, because p-value is less than 0.01 Fail to reject Ho, because -4.22 falls outside the…A professional racing team is holding tryouts at its test track. The team requires its drivers to have an average lap time of at most 133 seconds at its test track. The team will use a one sample z-test of significance to determine if they should hire a new driver. An amateur driver completes 8 timed laps of the test track with an average lap time of 136 seconds. If the standard deviation of all lap times at this track is 4.1 seconds, what is the value of the test statistic? Round your answer to two decimal places.