6. Gravetter/Wallnau/Forzano, Essentials - Chapter 8 - End-of-chapter question 9 The psychology department is gradually changing its curriculum by increasing the number of online course offerings. To evaluate the effectiveness of this change, a random sample of n = 36 students who registered for Introductory Psychology is placed in the online version of the course. At the end of the semester, all students take the same final exam. The average score for the sample is M = 76. For the general population of students taking the traditional lecture class, the final exam scores form a normal distribution with a mean of μ = 71. 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? Use a two-tailed test with α = .05. z-critical = ± z = These results indicate: Failure to reject the null hypothesis; the course has a significant effect Rejection of the null hypothesis; the course does not have a significant effect Failure to reject the null hypothesis; the course does not have a significant effect Rejection of the null hypothesis; the course has a significant effect

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 3E

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6. Gravetter/Wallnau/Forzano, Essentials - Chapter 8 - End-of-chapter question 9

The psychology department is gradually changing its curriculum by increasing the number of online course offerings. To evaluate the effectiveness of this change, a random sample of n = 36 students who registered for Introductory Psychology is placed in the online version of the course. At the end of the semester, all students take the same final exam. The average score for the sample is M = 76. For the general population of students taking the traditional lecture class, the final exam scores form a normal distribution with a mean of μ = 71.

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? Use a two-tailed test with α = .05.

z-critical	=	±
z	=

These results indicate:

Failure to reject the null hypothesis; the course has a significant effect

Rejection of the null hypothesis; the course does not have a significant effect

Failure to reject the null hypothesis; the course does not have a significant effect

Rejection of the null hypothesis; the course has a significant effect

If the final exam scores for the population have a standard deviation of σ = 18, does the sample provide enough evidence to conclude that the new online course is significantly different from the traditional class? Again, use a two-tailed test with α = .05. (Round z score to two decimal places.)

z-critical	=	±
z	=

These results indicate:

Failure to reject the null hypothesis; the course has a significant effect

Rejection of the null hypothesis; the course has a significant effect

Rejection of the null hypothesis; the course does not have a significant effect

Failure to reject the null hypothesis; the course does not have a significant effect

Comparing your answers for the two cases, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.

A smaller standard deviation produces a larger standard error, which reduces the likelihood of rejecting the null hypothesis.

A larger standard deviation produces a larger standard error, which reduces the likelihood of rejecting the null hypothesis.

A larger standard deviation produces a smaller standard error, which reduces the likelihood of rejecting the null hypothesis.

A smaller standard deviation produces a smaller standard error, which reduces the likelihood of rejecting the null hypothesis.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Given information

Sample mean = 76

Population mean µ = 71

Sample size = 36

Standard deviation = 12

Significance level (α) = 0.05

Null and Alternative Hypothesis

Null Hypothesis: -

H₀: µ = 71

Alternative Hypothesis:-

i.e. µ ≠ 71

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