Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the F table.) Treatments A B C D −7 −12 −9 −14 −8 −16 −13 −7 −10 −20 −13 −6 −15 −14 −14 Click here for the Excel Data File a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) b. Calculate SSTR and MSTR. (Round final answers to 4 decimal places.) c. Calculate SSE and MSE. (Round final answers to 4 decimal places.) d. Specify the competing hypotheses in order to determine whether some differences exist between the population means. multiple choice 1 H0: μA ≥ μB ≥ μC; HA: Not all population means are equal. H0: μA ≤ μB ≤ μC; HA: Not all population means are equal. H0: μA = μB = μC; HA: Not all population means are equal. Correct e-1. Calculate the value of the F(df1, df2) test statistic. (Round final answer to 3 decimal places.) e-2. Find the p-value. multiple choice 2 0.01 p-value < 0.025 Correct 0.05 p-value < 0.10 p-value 0.10 0.025 p-value < 0.05 p-value < 0.01 f. At the 5% significance level, what is the conclusion to the test? multiple choice 3 Reject H0 since the p-value is less than significance level Correct Do not reject H0 since the p-value is not less than significance level Do not reject H0 since the p-value is less than significance level Reject H0 since the p-value is not less than significance level g. Interpret the results at α� = 0.05. multiple choice 4 We cannot conclude that some means differ. We conclude that some means differ. Correct We conclude that all means differ. We conclude that population mean C is greater than population mean A.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 3CYU

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Related questions

Question

Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the F table.)

Treatments
A	B	C	D
−7	−12	−9	−14
−8	−16	−13	−7
−10	−20	−13	−6
	−15	−14
		−14

Click here for the Excel Data File

a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

b. Calculate SSTR and MSTR. (Round final answers to 4 decimal places.)

c. Calculate SSE and MSE. (Round final answers to 4 decimal places.)

d. Specify the competing hypotheses in order to determine whether some differences exist between the population means.

multiple choice 1

H₀: μ_A ≥ μ_B ≥ μ_C; H_A: Not all population means are equal.
H₀: μ_A ≤ μ_B ≤ μ_C; H_A: Not all population means are equal.
H₀: μ_A = μ_B = μ_C; H_A: Not all population means are equal. Correct

e-1. Calculate the value of the F_(df1, df2) test statistic. (Round final answer to 3 decimal places.)

e-2. Find the p-value.

multiple choice 2

0.01 p-value < 0.025 Correct
0.05 p-value < 0.10
p-value 0.10
0.025 p-value < 0.05
p-value < 0.01

f. At the 5% significance level, what is the conclusion to the test?

multiple choice 3

Reject H₀ since the p-value is less than significance level Correct
Do not reject H₀ since the p-value is not less than significance level
Do not reject H₀ since the p-value is less than significance level
Reject H₀ since the p-value is not less than significance level

g. Interpret the results at α� = 0.05.

multiple choice 4

We cannot conclude that some means differ.
We conclude that some means differ. Correct
We conclude that all means differ.
We conclude that population mean C is greater than population mean A.

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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