The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal. Teacher 1 Teacher 2 ?̅1 = 473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18 a. State the null and alternate hypotheses (write it mathematically) and write your claim. b. Find the test statistic c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical values. d. Decide whether to reject or fail to reject the null. e. Make an interpretation of your decision in the context.

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Description: The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teacher

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 results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal.

Teacher 1	Teacher 2
?̅1 = 473	?̅2 = 459
S₁ = 39.7	S₂ = 24.5
n ₁ = 8	n ₂ = 18

a. State the null and alternate hypotheses (write it mathematically) and write your claim.

b. Find the test statistic

c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical values.

d. Decide whether to reject or fail to reject the null.

e. Make an interpretation of your decision in the context.

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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