Q 20. Let u be the mean serum cholesterol level of the population of 20- to 74-year-old males in a particular countryμand we wish to test the null hypothesis Hoμ ≥ 220mg/100ml at the significance level a = 0.05. We knowthat the standard deviation of the population is o = 60mg/100ml, and the true population mean is as smallas 200mg/100ml.(a) Find the minimum sample size we need so that the power of the test can be at least 95%.(b) If the true population mean is 180mg/100ml instead of 200mg/100ml, describe how the significancelevel and power will be affected, i.e., increased, decreased or unchanged. Justify your answer.(c) If we decrease the significance level, will the power of test be increased? Justify your answer.

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Answered: Q 20. Let u be the mean serum…

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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A population of values has a normal distribution with μ=248.4μ=248.4 and σ=23.6σ=23.6. You intend to draw a random sample of size n=32n=32.Find P18, which is the score separating the bottom 18% scores from the top 82% scores.P18 (for single values) = Find P18, which is the mean separating the bottom 18% means from the top 82% means.P18 (for sample means) = Enter your answers as numbers accurate to 1 decimal place.************NOTE************ round your answer to ONE digit after the decimal point! ***********Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
A population of values has a normal distribution with μ=106.2μ=106.2 and σ=61σ=61. You intend to draw a random sample of size n=85n=85.Find P93, which is the score separating the bottom 93% scores from the top 7% scores.P93 (for single values) = Find P93, which is the mean separating the bottom 93% means from the top 7% means.P93 (for sample means) = Enter your answers as numbers accurate to 1 decimal place.
A population of N = 25 scores has ΣX = 40 and ΣX2= 120. For this population, what is the value of SS (sum of squared deviations)?
8,10
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.
26 The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α=0.01, can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal 0.37 0.75 0.60 0.49 2.66 1.18 0.33 0.46 0.46 1.64 0.33 0.50 0.58 0.41 1.39 (b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region. The degrees of freedom for the numerator, d.f.N, is ____ and the degrees of freedom for the denominator, d.f.D, is _____ The critical…
The average zinc concentration recovered from a sample of measurements taken in 40 different locations in a river is found to be 2.5 grams per milliliter. How large a sample is required if we want to be 95% confident that our estimate of ? is off by less than 0.05. Assume that the population standard deviation is 0.25 gram per milliliter.
2. Suppose the chamber of commerce at Pyramid Lake advertises that the average length of trout caught at the lake is μ = 19 inches. However, a fishing magazine survey reported that for a random sample of 51 fish caught, the mean length was x = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of the trout caught at Pyramid Lake is less than μ = 10 inches? (Use α = 0.05)
Let XXN(u. 16). How much should the sample size he for testing HeiH = 24 rs. He = 25 ata = 0.025 and ß = 0.409 (a) 77 (b) 48 (c) 35 (d) 28 (e) None
You wish to test Ho: μ₁ μ2 versus Ha:μ₁ μ₂ at a = = 0.10. You obtain a sample of size n₁ 1 = 58.2 and a standard deviation of $₁ = 20.9 from the first population. You obtain a sample 40.2 and a standard deviation of $2 = 5.6 from the second 9 with a mean of 2 a mean of of size n2 population. = = What is the test statistic? = = 6 with Assume that the data come from normal populations with equal variances. Round your answers to three decimal places, and round any interim calculations to four decimal places.
Question 7 > You wish to test the following claim (Ha) at a significance level of a = 0.05. H.: 41 Ha: µ1 7 42 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you have reason to believe that the variances of the two populations are equal. You obtain a sample of size nį = 14 with a mean of M1 first population. You obtain a sample of size n2 of SD2 = 7.4 from the second population. = 67.8 and a standard deviation of SD1 19 with a mean of M2 15.5 from the 61.7 and a standard deviation In the answer box below insert 2.0395 as the critical value for this test. (Report answer accurate to three decimal places.) critical value What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = %3D The test statistic is... O in the critical region O not in the critical region

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