Members of the school committee for a large city claim that the population mean class size of a middle school class within the district is exactly 20 students. Karla, the superintendent of schools for the city, thinks the population mean is less. She selects a random sample of 35 middle school classes across the city. The sample mean is 18.5 students with a sample standard deviation of 3.7 students. The test statistic t for a hypothesis test of H0:μ=20 versus Ha:μ<20 is t≈−2.40. If 0.01<p-value<0.025 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean class size of a middle school class within the district is less than 20 students? Select all that apply: A) Reject the null hypothesis that the true population mean class size of a middle school class within the district is equal to 20 students. B) Fail to reject the null hypothesis that the true population mean class size of a middle school class within the district is equal to 20 students. C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean class size of a middle school class within the district is less than 20 students. D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean class size of a middle school class within the district is less than 20 students.

Name: Members of the school committee for a large city claim that the popula
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Description: Members of the school committee for a large city claim that the population mean class size of a middle school class within the district is exactly 20 students. Karla, the superintendent of schools for the city, thinks the population mean is less. She

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Members of the school committee for a large city claim that the population mean class size of a middle school class within the district is exactly 20 students. Karla, the superintendent of schools for the city, thinks the population mean is less. She selects a random sample of 35 middle school classes across the city. The sample mean is 18.5 students with a sample standard deviation of 3.7 students. The test statistic t for a hypothesis test of H0:μ=20 versus Ha:μ<20 is t≈−2.40. If 0.01<p-value<0.025 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean class size of a middle school class within the district is less than 20 students?

Select all that apply:

A) Reject the null hypothesis that the true population mean class size of a middle school class within the district is equal to 20 students.

B) Fail to reject the null hypothesis that the true population mean class size of a middle school class within the district is equal to 20 students.

C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean class size of a middle school class within the district is less than 20 students.

D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean class size of a middle school class within the district is less than 20 students.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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