Answered: On the basis of this sample, can the…

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 psychologist has developed a standardized test for measuring the vocabulary skills of 4-year-old children. The scores on the test form a normal distribution with μ = 72 and σ = 12. A researcher would like to use this test to investigate the idea that children who grow up with no siblings develop vocabulary skills at a different rate than children in large families. A sample of n = 25 children is obtained, and the mean test score for this sample is 66. On the basis of this sample, can the researcher conclude that vocabulary skills for children with no siblings are significantly different from those of the general population? Test at the .01 level of significance.

For each problem students will write out all steps of hypothesis testing:

State the null and research hypotheses.
Set the level of risk associated with the null hypothesis.
Select the appropriate test statistic.
Compute the test statistic value (called the obtained value).
Determine the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic.
Compare the obtained value and the critical value.
Make your decision.

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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