Fundamentals of Statistics (5th Edition)

5th Edition

ISBN: 9780134508306

Author: Michael Sullivan III

Publisher: PEARSON

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Textbook Question

Chapter 11.3, Problem 1AYU

In Problems 1–6, assume that the populations are normally distributed

a. Tea whether μ₁ ≠ μ₂ at the α − 0.05 level of significance for the given sample data.
b. Construct a 95% confidence interval about μ₁ − μ₂.

	Sample 1	Sample 2
N	15	15
x ¯	15.3	14.2
S	3.2	3.5

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter 11.2, Problem 18AYU

Chapter 11.3, Problem 2AYU

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6) Use a significance level of a = 0.05 to test the claim that µ # 32.6. The sample data from normal population consists of 15 scores for which x = 41.9 and s = 7.7.

2. You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. H0:μ1=μ2H0:μ1=μ2 Ha:μ1≠μ2Ha:μ1≠μ2You believe both populations are normally distributed, but you do not know the standard deviations for either.You obtain a sample of size n1=13n1=13 with a mean of M1=66.5M1=66.5 and a standard deviation of SD1=14.8SD1=14.8. You obtain a sample of size n2=20n2=20 with a mean of M2=58.4M2=58.4 and a standard deviation of SD2=8.4SD2=8.4. test statistic = [three decimal accuracy] p-value = [three decimal accuracy] The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null hypothesis fail to reject the null hypothesis As such, the final conclusion is that... There is sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean. There is not sufficient sample evidence to support the claim that the first…

You wish to test the following claim (H1) at a significance level of α=0.05. Ho:μ1=μ2 H1:μ1≠μ2You 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 n1=17 with a mean of M1=63.1 and a standard deviation of SD1=18.7 from the first population. You obtain a sample of size n2=10 with a mean of M2=86.5 and a standard deviation of SD2=12.6 from the second population.What is the critical value for this test? (Report answer accurate to four decimal places.)critical value = ±What is the test statistic for this sample? (Report answer accurate to four decimal places.)test statistic = The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is…

Chapter 11 Solutions

Fundamentals of Statistics (5th Edition)

Ch. 11.1 - A sampling method is _____ when the individuals...Ch. 11.1 - A sampling method is _____ when the individuals...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - Prob. 8AYU Ch. 11.1 - In Problems 912, conduct each test at the = 0.05...Ch. 11.1 - In Problems 912, conduct each test at the = 0.05...

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In Problems 1–6, assume that the populations are normally distributed 1. a. Tea whether μ 1 ≠ μ 2 at the α − 0.05 level of significance for the given sample data. b. Construct a 95% confidence interval about μ 1 − μ 2 . Sample 1 Sample 2 N 15 15 x ¯ 15.3 14.2 S 3.2 3.5

Solution Summary: The author concludes that there is no sufficient evidence to support the claim that "there is a difference between two population means".

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Chapter 11 Solutions