Construct a 99 % confidence interval for the difference between the mean lifetimesof two kinds of light bulbs, given that a random sample of 40 light bulbs of thefirst kind lasted on the average 41 hours of continuous use and 50 light bulbs ofthe second kind lasted on the average 40. hours of continuous. use. The populationstandard deviations are known to be o1 = 26 and o2 = 22.Solution For a = 0.06, we find from Table III that z0.03 =94% confidence interval for µi –1.88. Therefore, theuz is262(418 - 402) – 1.88 ·V 40.222< H1 - 4250262222+40< (418 – 402) +1.88 ·50

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Answered: Construct a 99 % confidence interval…

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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4
the life of a certain model of phone is normally distributed with an average of 30 months and a standard deviation of 6 months. In a sample of 65 phones, what is the approximate number that last between 28 months and 34 months?
Independent random samples from two normally distributed populations give the following results:nx = 10 x̄ = 480 sx = 30ny = 12 ȳ = 520 sy = 25a. If we assume that the unknown population variances are equal, find the 90% confidence interval for the difference of population means.b. If we do not assume that the unknown population variances are equal, find the 90% confidence interval for the difference between population means.
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Hawaiians are known to have an active lifestyle, enjoying the fresh air and natural beauty the islands have to offer. The life expectancy of the US population across all 50 states is µ=78.62 years with a standard deviation σ=16.51 years. A randomly selected sample of 100 Hawaiians show an average life expectancy x̅=82.52 years. Is Hawaiians’ average life expectancy significantly different from 78.62, assuming α=0.01?
a. What are the sample estimates of β0,β1,and β2? b. What is the least squares prediction equation? c. FindSSE,MSE,and standard deviation . Interpret the standard deviation in the context of the problem. d. Test H0: β1=0 against Ha: β1≠0.Use α=0.01. e. Use a 95% confidence interval to estimate β2. f. Find R2 and R^2_a and interpret these values. g. Find the test statistic for testing H0: β1=β2=0. h. Find the observed significance level of the test in part g.interpret the result.
A sample of 10 from population 1 has a mean of 32 and a standard deviation of 6. A sample of 13 from population 2 has a mean of 48 and a standard deviation of 8. The population standard deviations are unknown but assumed to be equal. Test the hypothesis, at the 1% level of significance, that the population means are the same. State your conclusion as a sentence and include the test statistic and the critical value.
A random sample of size 35, taken from a normal population with a variance of 5, has a mean of 80. A second random sample of size 36, taken from a different normal population with a variance of 3, has a mean of 75. Find a 95% confidence interval for μ1 − μ2.
Currently patrons at the library speak at an average of 68 decibels. Will this average decline after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 60 people speaking at the library. Their average decibel level was 63.5 and their standard deviation was 15. What can be concluded at the the αα = 0.05 level of significance?The null and alternative hypotheses would be: H0:H0: Mean = __?__orrect H1:H1: Mean < __?__orrectC The test statistic t= __?__ (please show your answer to 3 decimal places.) The p-value = __?__ (Please show your answer to 4 decimal places.)
4.2 A sample of 19 female bears was measured for chest girth (y) and neck girth (x), both in inches. The least squares regression equation relating the two variables is = 5.32 + 1.53 x. The standard deviation of the regression is s = 3.692. y^ 4.2.1 What is a 95% confidence interval for the average (or mean) chest girth for bears with a neck girth of 20 inches? The standard error of the fit is s.e.(fit) = 0.880 a. (27.9, 43.9) b. (28.1, 43.7) c. (34.1, 37.8) d. None of the above 4.2.2 Interpret the confidence interval obtained in 4.2.1
Currently patrons at the library speak at an average of 64 decibels. Will this average change after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 69 people speaking at the library. Their average decibel level was 61.7 and their standard deviation was 6. What can be concluded at the α = 0.05 level of significance? H0:H0: ? μ p Select an answer > ≠ < = H1:H1: ? p μ Select an answer = > < ≠ The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.)
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.

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