1. A car dealer claims that the average price of Honda Vios is at least 662,000.00. A client suspected thatthe claim is incorrect and found that random sample of 15 similar vehicles has the mean price of$640,000.00 and standard deviation of 24,000.00. Is there enough evidence to reject the dealer's claimat x = 0.05?From the given problem #1 discuss the following:1. define and illustrate the nulI hypothesis, alternative hypothesis, level of significance. (Provideexplanation)2. identify the parameter to be tested. (Provide Explanation)3. identify the appropriate form of test statistics. (Provide Explanation)4. identify the rejection and non-rejection regions and the critical values. (Provide Explanation)5. Make a conclusion base from the result you obtain (Some of the examples can be found in 4th quartermodule 1). (Provide Explanation)6. identify if it is a Type I and Type Il errors in claims and decisions (Provide Explanation)

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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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It is known that the mean time taken for a taco delivery from a taco shop is 18.4 minutes and the standard deviation is 2.4 minutes. The taco shop wants to promote the business by guaranteeing a maximum waiting time for its cus- tomers. If a taco delivery is not serviced within that period, the customer will receive 42% discount on the charges. The company wants to limit this dis- count to at most 5% of the customers. What should the maximum guaranteed waiting time be?
A manufacturer claims that the mean lifetime, p, of its light bulbs is 42 months. The standard deviation of these lifetimes is 5 months. Sixty bulbs are selected at random, and their mean lifetime is found to be 44 months. 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 H,. Az Ho: H : (b) Determine the type of test statistic to use. 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.) and | (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 42 months? O…
1. A random sample of 30 warehouses was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each warehouse in the sample for the March quarter of 2019. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed, calculate a 99% confidence interval for the mean usage in the March quarter of 2019.
It is necessary for an automobile producer to estimate the number of miles per gallon achieved by its cars. Suppose that the sample mean for a random sample of 110 cars is 29.4 miles and assume the standard deviation is 3.4 miles. Now suppose the car producer wants to test the hypothesis that ?μ, the mean number of miles per gallon, is 32.4 against the alternative hypothesis that it is not 32.4 Conduct a test using ?=.05 by giving the following: (a) positive critical ? score (b) negative critical ? score (c) test statistic The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that ?=32.4B. We can reject the null hypothesis that ?=32.4 and accept that ?≠32.4
Suppose that scores on a particular test are normally distributed with a mean of 120 and a standard deviation of 16. What is the minimum score needed to be in the top 10% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
A battery manufacturer claims that the lifetime of a certain type of battery has a population mean of 40 hours and a standard deviation of 5 hours. Let Y represent the mean lifetime of the batteries in a simple random sample of size 100. If the claim is true, what is P(X < 36.7)? a. b. Based on the answer to part (a), if the claim is true, is a sample mean lifetime of 36.7 hours unusually short? If the sample mean lifetime of the 100 batteries were 36.7 hours, would you find the manufacturer's claim to be plausible? Explain. c. d. If the claim is true, what is P(X < 39.8)? Based on the answer to part (d), if the claim is true, is a sample mean lifetime of 39.8 hours unusually short? e. If the sample mean lifetime of the 100 batteries were 39.8 hours, would you find the manufacturer's claim to be plausible? Explain. f.
iii
Suppose that scores on a particular test are normally distributed with a mean of 120 and a standard deviation of 16. What is the minimum score needed to be in the top 15% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
2) The manufacturer of a certain brand of automobiles component claims that mean life of these component is 70 months. An independent agency wants to check this claim and took a random sample of 40 components and found that the mean life for this sample is 67 months with a standard deviation of 5 months. At 5% LOS, can we conclude that the mean life of these component is less than 70 months?
A cereal manufacturer wants to test the performance of one of the packaging filling machines in his factory. This machine is designed to fit an average of 15 ounces of cereal into each box, and manufacturers want to detect any deviation from this setting. This quality study is conducted by taking a random sample of 100 boxes from today's production, and then determining whether the average content of all samples is the correct 15 ounces per box. From the sample obtained an average result of 14.85 ounces with a standard deviation of 0.55 ounces. Test the hypothesis for this study using = 2%

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