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Find the sample statistics, test statistic, p-value, critical region(s) and draw the normal curve for the question

Find the sample statistics, test statistic, p-value, critical region(s) and draw the normal curve for the question

MATLAB: An Introduction with Applications
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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Find the sample statistics, test statistic, p-value, critical region(s) and draw the normal curve for the question 

A researcher is investigating the impact of preschool on the development of young children. The main question is whether children who spend more time away from their mothers are more or less likely to exhibit developmental problems in kindergarten. Using a standardized scale, the average rating of behavioral problems in kindergarten children is 36.6, with a standard deviation of 8. A random sample of 15 kindergarten children, who had spent at least 20 hours per week in childcare during the previous year, produced the scores listed below. The objective is to test, at a 0.01 level of significance, whether children who spend more time away from their mothers are more likely to demonstrate developmental problems in kindergarten. The scores from the sample are as follows: 38, 39, 42, 43, 48, 44, 38, 36, 42, 37, 36, 47, 48, 38, 41
Transcribed Image Text:A researcher is investigating the impact of preschool on the development of young children. The main question is whether children who spend more time away from their mothers are more or less likely to exhibit developmental problems in kindergarten. Using a standardized scale, the average rating of behavioral problems in kindergarten children is 36.6, with a standard deviation of 8. A random sample of 15 kindergarten children, who had spent at least 20 hours per week in childcare during the previous year, produced the scores listed below. The objective is to test, at a 0.01 level of significance, whether children who spend more time away from their mothers are more likely to demonstrate developmental problems in kindergarten. The scores from the sample are as follows: 38, 39, 42, 43, 48, 44, 38, 36, 42, 37, 36, 47, 48, 38, 41
Expert Solution
Step 1

From the given sample data : n=15 , ƩX= 617

Therefore ,

The sample mean is , X¯=∑Xn=61715=41.13

Also given :  σ=8 , μ0=36.6 , α=0.01

Since , the population standard deviation (σ) is known.

Therefore , use normal-distribution.

Our aim is to test the claim that children who spend more time away from their mothers are more likely to show developmental problem in kindergarten.

Here , we use the one sample mean Z-test.

 

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