a. What are the null and alternative hypotheses?b. The test statistic, t, is c. The P-value isd. State the conclusion for the test.e. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean. Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue backgroundwere given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. Theresearchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normallydistributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b).Click the icon to view the summary statistics.a. Use a 0.05 significance level to test the claim that blue enhances performance on a creative task.What are the null and alternative hypotheses?A. Ho: H₁ H₂H₁: H₁

Background μ n x¯ s Blue μ1 31 3.62 0.51 Red μ2 36 2.92 0.88

Answered: Researchers conducted trials to…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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Related questions

Question

a. What are the null and alternative hypotheses?

b. The test statistic, t, is

c. The P-value is

d. State the conclusion for the test.

e. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background
were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The
researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally
distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b).
Click the icon to view the summary statistics.
a. Use a 0.05 significance level to test the claim that blue enhances performance on a creative task.
What are the null and alternative hypotheses?
A. Ho: H₁ H₂
H₁: H₁ <H₂
C. Ho: ₁²₂
H₁: M₁ <H₂
Response Summary Statistics
Background
Blue
Red
μ
H₁
H₂
n
X
S
31
3.62 0.51
36 2.92 0.88
B. Ho: ₁ = 2
H₁ H₁ H₂
D. Ho: M₁ = H₂
H₁: H₁ H₂
-
X

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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