Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessiveshrinkage or is discolored. Two random samples, each of size 300, are selected, and 15 defective parts are found in the sample frommachine 1, while 8 defective parts are found in the sample from machine 2. Suppose that p₁ -0.05 and p2 -0.01.(a) With the sample sizes given, what is the power of the test for this two sided alternative? Power =Round your answer to three decimal places (e.g. 98.765).(b) Determine the sample size needed to detect this difference with a probability of at least 0.9. Use a = 0.05.n=Round your answer up to the nearest integer.Statistical Tables and Charts

Given Information: Machine 1: Sample size n1=300 Number of defectives x1=15 Proportion p1=0.05…

Answered: Two different types of…

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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Suppose we have a population of N=4 measurements given by 2,4 , 6 and 8 a. List all possible simple random samples of size n32 b. Show that E(y ) = p
Packages of mixed nuts made by a certain company contain four types of nuts. The percentages of nuts of Types 1, 2, 3, and 4 are suppased to be 40%, 30%, 20%, and 10%s, respectively. A random sample of nuts is selected, and each cne is categorized by type. (a) If the sample size is 150 and the resulting test statistic value is x - 19.0, what condlusion wauld be appropriate for a significance level of 0.001? O Reject Ha O Fail to reject Hg (b) If the random sample had consisted of only 40 nuts, would you use the chi-square test here? O Yes O No
Suppose a simple random sample of size n=50is obtained from a population whose size is N=20,000 and whose population proportion with a specified characteristic is p=0.6. Complete parts (a) through (c) below.
A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of n1 = 16 locations in region I gave the following information about the number of cases of fox rabies near that location. x1: Region I Data 2 8 8 8 6 8 8 1 3 3 3 2 5 1 4 6 A second random sample of n2 = 15 locations in region II gave the following information about the number of cases of fox rabies near that location. x2: Region II Data 1 1 5 1 4 8 5 4 4 4 2 2 5 6 9 (i) Use a calculator with sample mean and sample standard deviation keys to calculate x1 and s1 in region I, and x2 and s2 in region II. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is…
A study of fox rabies in southern Germany gave the following information about different regions and the occurrence of rabies in each region. A random sample of n1 = 16 locations in region 1 gave the following information about the number of cases of fox rabies near that location. x1: Region I Data 3 7 8 7 5 8 8 1 3 3 3 2 5 1 4 6 A second random sample of n2 = 15 locations in region II gave the following information about the number of cases of fox rabies near that location. x2: Region II Data 4 2 4 1 3 8 5 4 4 4 2 2 5 6 9 Note: If a two-sample t-test is appropriate, for degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.Use a calculator with sample mean and sample standard deviation keys to find x1 and s1 in region I, and x2 and s2 in region II. (Round your answers to two…
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
Suppose a simple random sample of size n equals 1000 is obtained from a population whose size is N equals 2 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.75. Complete parts (a) through (c) below.
A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of n1 = 16 locations in region I gave the following information about the number of cases of fox rabies near that location. x1: Region I Data 1 9 9 9 7 8 8 1 3 3 3 2 5 1 4 6 A second random sample of n2 = 15 locations in region II gave the following information about the number of cases of fox rabies near that location. x2: Region II Data 1 1 5 1 6 8 5 4 4 4 2 2 5 6 9 What is the value of the sample test statistic? (Test the difference μ1 − μ2. Do not use rounded values. Round your final answer to three decimal places.)
9. Let 7 = 1.135013 be the sample mean of an iid sample r1,..., T50 from a gamma population Gamma(1, 3). Here ß > 0 is the unknown paramcter of interest. Construct an approximate 95%-CI for ß.
In a 4-week study about the effectiveness of using magnetic insoles to treat plantar heel pain, 51 subjects wore magnetic insoles and 47 subjects wore nonmagnetic insoles. The results are shown at the right. At α=0.06, can you support the claim that there is a difference in the proportion of subjects who feel better between the twogroups? Assume the random samples are independent. Complete parts (a) through (e).
Qn5. Using the Kruskal-Wallis test at a = 0.01, can we conclude that the three populations represented by the three samples differ with respect to propellant burning rates? A Summarized data is given as follows: For System I: n = 5, Sum of the ranks i.e., R = 58 For System II:n, = 6, Sum of the ranks i.e., R, = 24 For System III: n, = 8, Sum of the ranks i.e., R, = 87. %3! ( Given that Table value of Chi Square = 9.21)

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