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.

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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