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

See similar textbooks

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.

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