Answered: is this result sufficient to conclude…

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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Question

Please use the following information to answer 11a-11c:

Montarello and Martens (2005) found that fifth-grade students completed more matematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics acheivement test that produces a normal distribution of scores with a mean of µ = 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions, and gives the modified test to a sample of n = 36 students. If the average test score for the sample is x̅ = 104, is this result sufficient to conclude that inserting the easy questions improves performance? Use a one-tailed test with α = .01.

11a. Which of the following correctly represents the null and alternative hypothesis for the mentioned sample of n =36 (MUST SHOW WORK FOR THIS PROBLEM)?

a. Ho: µ = 100, H_1:µ ≠ 100

b. Ho: µ > 100, H_1:µ ≤ 100

c. Ho: µ ≤ 100, H_1:µ > 100

d. Ho: µ ≥ 100, H_1:µ < 100

11b. Which of the following represents the critical region for this mentioned sample (MUST SHOW WORK FOR THIS PROBLEM)?

a. z = 2.33

b. z = ±2.33

c. z = 2.58

d. z = ±2.58

11c. Compute the test statistic(z-observed) for the mentioned sample (MUST SHOW WORK FOR THIS PROBLEM).

Note: Must show calculations for standard error alongside the calculations for the test statistic.

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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