(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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An SRS of 450 high school seniors gained an average of x = 20.80 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation a = 54.81. We want to estimate the mean change in score in the population of all high school seniors. (a) Using the 68-95-99.7 Rule or the z-table (Table A), give a 68% confidence interval (a, b) for u based on this sample. H (Enter your answers rounded to three decimal places. If you are using Crunchlt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.) a: (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? The interval does not contain 0, so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0. We cannot be certain at all. If we want…
An inventor has developed a new, energy-efficient lawn mower engine. He claims that the engine will run continuously for 5 hours (300 minutes) on a single gallon of regular gasoline. From his stock of 2000 engines, the inventor selects a simple random sample of 40 engines for testing. The engines run for an average of 295 minutes, with a standard deviation of 20 minutes. Test the null hypothesis that the mean run time is µ = 305 minutes against the alternative hypothesis that the mean run time is not 305 minutes. Use p = .08. (Assume that run times for the population of engines are normally distributed.) SE = s / √( n ) t = (x - μ) / SE Compute the standard error (SE) _____________ Degrees of freedom (df) ___________________ t-test statistic (t) __________________________
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. H0: μ ≥ 220 H1: μ < 220 (a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.
The mean number of sick days taken by employees in a year is 6. Members of the Human Resources department believe that employees take more than 6 sick days. A random sample of 52 employees had a mean of 6.42 sick days with a standard deviation of 1.6 days. Test the group’s claim at α = 0.05. (a) Write the null and alternative hypotheses. (b) Find the test statistic, t0. (write the answer as a decimal rounded to 4 decimal places) (c) Approximate the P-value. (write the answer as a decimal rounded to 4 decimal places)
A nutritionist claims that the mean tuna consumption by a person is 3.2 pounds per year. A sample of 80 people shows that the mean tuna consumption by a person is 2.9 pounds per year. Assume the population standard deviation is 1.23 pounds. At α=0.07, can you reject the claim? (a) Identify the null hypothesis and alternative hypothesis. (b) Identify the standardized test statistic. z= (c) Find the P-value.
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…
Please help show me how to get the values of t= and P-value
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