1.) What are the assumptions of a two-sample t-test? Select all that apply below A) Both samples were obtained using a random sampling method. B) The observations in one sample are independent of the observations in the other sample. C) Both samples are approximately normally distributed. D) Both samples have approximately the same variance. E) Both samples have approximately the same mean. 2.) What is the critical value of t with α=0.1 for this test? Give your answer to two decimal places. 3.) What is the most precise P-value that you can determine for this test? 4.) What can you conclude about the difference between the older and younger people in how often they dream in color? Interpret the conclusions of the test in terms of the original scientific question. Until the mid 21st century, it was thought that humans dreamed in black and whiterather than color. A recent hypothesis is that North Americans did in fact dream inblack and white in the era of black-and-white television and movies, but that weshifted back to dreaming in color after the introduction of color media.To test this hypothesis, Murzyn (2008) queried 30 older individuals who had grownup in the black-and-white era and 30 younger individuals who grew up with colormedia about their dreams. She recorded the percentage of color dreams for eachindividual.A mean of 68.4% of the younger peoples' dreams were in color (with a standarddeviation of 31.8%). On average, 33.9% of the older individuals' dreams were incolor, with a standard deviation of 36.9%. The scores were approximately normallydistributed in each group.Is the difference between the two means statistically significant? Answer thefollowing questions as you perform a two-sample t-test for this comparison.

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Answered: 1.) What are the assumptions of a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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1.) What are the assumptions of a two-sample t-test? Select all that apply below

A) Both samples were obtained using a random sampling method.

B) The observations in one sample are independent of the observations in the other sample.

C) Both samples are approximately normally distributed.

D) Both samples have approximately the same variance.

E) Both samples have approximately the same mean.

2.) What is the critical value of t with α=0.1 for this test? Give your answer to two decimal places.

3.) What is the most precise P-value that you can determine for this test?

4.) What can you conclude about the difference between the older and younger people in how often they dream in color? Interpret the conclusions of the test in terms of the original scientific question.

Until the mid 21st century, it was thought that humans dreamed in black and white
rather than color. A recent hypothesis is that North Americans did in fact dream in
black and white in the era of black-and-white television and movies, but that we
shifted back to dreaming in color after the introduction of color media.
To test this hypothesis, Murzyn (2008) queried 30 older individuals who had grown
up in the black-and-white era and 30 younger individuals who grew up with color
media about their dreams. She recorded the percentage of color dreams for each
individual.
A mean of 68.4% of the younger peoples' dreams were in color (with a standard
deviation of 31.8%). On average, 33.9% of the older individuals' dreams were in
color, with a standard deviation of 36.9%. The scores were approximately normally
distributed in each group.
Is the difference between the two means statistically significant? Answer the
following questions as you perform a two-sample t-test for this comparison.

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.

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