(c)The solar water heater manufacturers claim that the mean life of the heater is less than760 hours. A random sample of 28 solar water heaters is drawn from the production lineevery day with a standard deviation of 60 hours. Use a = 0.05.(i) Write the null and alternative hypotheses(ii) Find the when the test value is -1.703.(iii) Conduct a hypothesis test using p-value approach.(iv) Do you have enough evidence to reject the manufacturers' claim?(v) What is the probability of committing type 1 error?

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Answered: (c) The solar water heater…

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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humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 61 It has long been stated that the mean temperature healthy adults 1 to 4 times daily for 3 days, obtaining 275 measurements. The sample data resulted in a sample mean of 98.3°F and a sample standard deviation of 1°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the a = 0.01 level of significance. State the hypotheses Họ: H 98.6°F H: H 98.6°F Find the test statistic. (Round to two decimal places as needed.) The P-value is. (Round to three decimal places as needed.) What can be concluded? What can be concluded? A. Reject Ho since the P-value is not less than the significance level. B. Reject Ho since the P-value is less than the significance level. C. Do not reject H, since the P-value is not less than the significance level. D. Do…
BIG Corporation advertises that its light bulbs have a mean lifetime, µ, of at least 3000 hours. Suppose that we have reason to doubt this claim and decide to do statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample 2860 hours and that the sample standard deviation of the lifetimes is 600 hours. Based on this information, answer thi questions below. What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test? H0 : µ is ____ ? _____ H1: µ is ____ ? ____ In the content of this test, what is a Type I error? A Type I error is ________ the hypothesis that µ is? _______ ?_______ when, in fact, µ is ? _______ Suppose that we decide to reject the null hypothesis. What sort of error might we be making? ______
It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 50 healthy adults 1 to 4 times daily for 3 days, obtaining 225 measurements. The sample data resulted in a sample mean of 98.4°F and a sample standard deviation of 1°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the oa = 0.01 level of significance. State the hypotheses. Ho: H = 98.6°F H1: H < 98.6°F Find the test statistic. tn = - 3.00 (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.)
The sample mean and standard deviation from a random sample of 32 observations from a normal population were computed asx =25 and s = 10. Calculate the t statistic of the test required to determine whether there is enough evidence to infer at the 8% significance level that the population mean is greater than 22.Test Statistic =
The manager of a warehouse store wants to estimate the average number of laser printer toner cartridges sold each day. A random sample of 37 days is selected and the sample mean is 115. The population standard deviation is estimated to be 9.8. Test the claim, using a 95% confidence interval for the mean, that the average number of laser printer toner cartridges sold each day is 110.
The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with = 0.2 kg. Let μ denote the true average weight reading on the scale. (a) What hypotheses should be tested? (b) What is the p-value when = 9.85? What would you conclude at significance level a = 0.01?
The ages of registered voters in Smith County are normally distributed with a population standard deviation of 3 years and an unknown population mean. A random sample of 18 voters is taken and results in a sample mean of 55 years. Find the margin of error for a 95% confidence interval for the population mean. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.
A sample of 12 concrete specimens from supplier A were tested for their compressive strength. The results gave an average of 85 MPa and a standard deviation of 4 MPa. From supplier B, 10 specimens were similarly tested and gave an average compressive strength of 81 MPa and a standard deviation of 5 MPa. (a) Using procedures of Hypothesis Testing, can we conclude at the 0.05 level of significance that the compressive strength of concrete from A exceeds that from B by more than 2 MPa? Assume the populations to be approximately normal with equal variances. (b) Is the assumption of equal variances in (a) justifiable at an a = 0.10?
In a left-tailed hypothesis for a population mean where the population standard deviation is unknown, the test statistic for a random sample size 18 was calculated to be -4.0545. Determine the P-value for the test. X
A simple random sample from a population with a normal distribution of 97 body temperatures has x=98.20°F and s=0.63°F. Construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans.
An SRS of 400 high school seniors gained an average of x = 21.87 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation o = 48.66. We want to estimate the mean change in score µ in the population of all high school seniors. (a) Using the 68-95-99.7 Rule or the z-table (Table A), give a 95% confidence interval (a, b) for u based on this sample. (Enter your answers rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.) a: b: (b) Based on your confidence interval in part (a), how certain are you that the mean change in score u in the population of all high school seniors is greater than 0? O The upper endpoint of the interval is larger than 0, so we are 95% certain that the mean change in score in the population of all high school seniors is greater than 0. O We cannot be…
In the past, the mean running time for a certain type of flashlight battery has been 9.6 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has decreased as a result. A hypothesis test is to be performed. Determine the null and alternative hypotheses. A. H0: µ ¥ 9.6 hours and H1: µ = 9.6 hours B. H0: µ = 9.6 hours and H1: µ ¥ 9.6 hours C. H0: µ = 9.6 hours and H1: µ > 9.6 hours D. H0: µ = 9.6 hours and H1: µ < 9.6 hours

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