The mean exam score for 44. male high school students are 19.9 and the population standard deviation is 5.2. The mean exam score for 55female high school students is 19.4 and the population standard deviation is4.9. At α=0.01, can you reject the claim that male and female high school students have equal exam scores? Complete parts (a) through (e). (a) Identify the claim and state H0 and Ha. What is the claim? A.Male high school students have lower exam scores than female students. B.Male and female high school students have different exam scores. C.Male and female high school students have equal exam scores. D.Male high school students have greater exam scores than female students. What are H0 and Ha? Find the critical value(s) and identify the rejection region(s).The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.

Given information: Sample size of males n1=44 Mean exam score for males X¯1=19.9 Standard deviation of exam score for males s1=5.2 Sample size of females n2=55 Mean exam score for females X¯2=19.4 Standard deviation of exam score for females s2=4.9 Significance level α=0.01(a) The claim states that male and female high school students have equal exam scores. Therefore the correct answer is option C. The hypotheses are defined as follows: H0:μ1=μ2Ha:μ1≠μ2 This corresponds to a two-tailed test, for which a z-test for two population means, with known population standard deviations will be used.The critical value, at 0.01 significance level, for a two-tailed test is: zc=±2.5758 Therefore, the rejection region for this two-tailed are the values that are greater than 2.5758 or the values that are less than -2.5758. The test statistic is calculated as: z=X¯1-X¯2σ12n1+σ22n2=19.9-19.45.2244+4.9255=0.4877 Since the test statistic (0.4877) is less than the critical value (2.5758), therefore, there is insufficient evidence to reject the null hypothesis. Hence, it can be concluded that there is enough evidence to support the claim that male and female high school students have equal exam scores.

Answered: The mean exam score for 44. male high…

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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The mean exam score for 44. male high school students are 19.9 and the population standard deviation is 5.2. The mean exam score for 55
female high school students is 19.4 and the population standard deviation is

4.9. At α=0.01, can you reject the claim that male and female high school students have equal exam scores? Complete parts (a) through (e).

(a) Identify the claim and state H0 and Ha.

What is the claim?

Male high school students have lower exam scores than female students.

Male and female high school students have different exam scores.

Male and female high school students have equal exam scores.

Male high school students have greater exam scores than female students.

What are H0 and Ha?

Find the critical value(s) and identify the rejection region(s).

The critical value(s) is/are

Find the standardized test statistic z for μ1−μ2.

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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