Answered: What is critical value of z? 2.…

Name: A researcher knows the scores on a creativity test are normally distri
Uploaded: 2024-03-20T07:07:12.000Z
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Description: A researcher knows the scores on a creativity test are normally distributed with u=60 and a=20. He wants to know if an art set given to children will improve scores on the creativity test. He gives a sample of n=49 children the art set and calculat

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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A researcher knows the scores on a creativity test are normally distributed with u=60 and a=20. He wants to know if an art set given to children will improve scores on the creativity test. He gives a sample of n=49 children the art set and calculates the sample mean (M=80) for his group of children that received the toy. He wants to evaluate if the toy resulted in significantly improves scores on creativity test. Use a p value of .05

1. What is critical value of z?

2. Compute the test statistic (z-statistic)

3. 2-3 sentences on write up of results.

4. What would type 1 error be in the context of this example?

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 + ...

Expert Solution

Step 1

Hi, the question have more than 3 parts. As per the guidelines I am obliged to answer first three parts only.

The test need to be conducted to check whether the mean score on a creativity test has increased from 60 or not. Thus right tail test need to be conducted.

The critical value of z at 0.05 level of significance from the standard normal table will be:

$z_{0.05} = 1.645$

Step 2 (2)

The test statistics can be calculated as:

Thus, the test statistics is 7

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