Essentials of Statistics for the B...

8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

A local college requires an English composition course for all freshmen. This year they are evaluating a new online version of the course. A random sample of n = 16 freshmen is selected and the students are placed in the online course. At the end of the semester, all freshmen take the same English composition exam. The average score for the sample is M = 76. For the general population of freshmen who look the traditional lecture class, the exam scores form a normal distribution with a mean of μ = 80.

a. If the final exam scores for the population have a standard deviation of σ = 12, does the sample provide enough evidence to conclude that the new online course is significantly different from the traditional class? Assume a two-tailed test with α = .05.

c. If the population standard deviation σ = 6, is the sample sufficient to demonstrate a significant difference? Again, assume a two-tailed test with α = .05.

c. Comparing your answers for pans a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.

To determine

To check: Whether the sample provides enough evidence to conclude that the new online course is significantly different from the traditional class, when σ=12.

Explanation

Given info:

Samples mean (M) is 76, population mean is 80, standard deviation is 12, alpha level is 0.05 and sample size is 16.

Calculation:

The null hypothesis states that there is no effect of the treatment and alternative hypothesis states opposite of null hypothesis. As given in the question that population mean is 80 and two tailed test is used, so the null hypothesis and alternative hypothesis for this question are:

H0: μ=80H1: μ≠80

The alpha level is given in the question as 0.05 and need to find boundaries of the critical region. As given in the question that two tailed hypothesis test used, so acceptance region is:

p=1−α2=1−0.052=1−0.025=0.975

The z-score critical value at 0.975 or at α=0.05 is ±1.96 using the z table. The z-score from given data is calculated as:

z=M−μσM

Where σM is known as standard error and calculated as

σM

To determine

The sample provides enough evidence to conclude that the new online course is significantly different from the traditional class, when σ=6.

To determine

To explain: The change in magnitude of the standard deviation influences the outcome of a hypothesis test.

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Essentials of Statistics for the B...

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Statistics Essentials of Statistics for the Behavioral Sciences 8th Edition