How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars) II III IV 27.9 13.6 22.6 17.3 23.5 9.7 20.5 16.3 14.9 11.1 7.3 14.5 8.6 8.1 12.7 15.5 11.5 6.5 19.6 7.5 10.9 9.8 Shall we reject or not reject the claim that there is no difference In population mean annual profits per employee in each of the tour types of companies? Use a 5% level of signiticance. (a) What is the level of significance? State the null and alternate hypotheses. O H H- H2- H - Hai H: Exactly two means are equa. O H: - H, - = Hai H, All four means are different. O I: , 2 a Hai H,: Exactly three means are equal. O H. - H2 = l, = Hai H: Not all the mcans are equal. (b) Find SSTor SSET and SSw SS ToT SS ET and check that SSTOT = SSar + SS w (Usc 3 decimal places.) TOP SSw= Find d.t. pET d.t. w MS prT MS ET and MS (Usc 3 decimal places for MSarn and MSw) df er BET dr MS BET MS W

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question
Find the value of the sample F statistic, (Use 3 decimal places.)
What are the degrees of freedom?
(numerator)
(denominator)
(c) Find the P-value of the sample test statistic.
O p-value > 0.100
O 0.050 < p-value < 0.100
O 0.025 < p-value < 0.0050
O 0.010 < p-value < 0.025
O 0.001 < p-value < 0.010
O P-value < 0.001
(d) Based on your answers in parts (a) to (c), will you reject ar fail to reject the null hypothesis?
O Since the p-value is greater than the level of significance al a = 0.05, we do not reject H.
O Since the p-value is less than or equal to the level of significarnce at a- 005, we reject H
O Since the p-value is greater than the level of significance at a = 0.05, wc reject
O Since the P valuc is less than or equal to the level of significance at a = 0.05, we do not reject. H
(e) Interpret your conclusion in the context of the application.
O At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.
O At the 5% level of significance there is sufficient evidence to conclude that the means are all equal.
O At the 5% level of significance there is insufficient evidence to conclude that the means are all equal.
O At the 5% level of significance there Is sufficient evidence to conclude that the means are not all equal.
(f) Make a summary table for your ANOVA test.
Source of
Sum of
Degrees of
P Value
Test
MS
P Type here to search
75°F Mostly sunny
Transcribed Image Text:Find the value of the sample F statistic, (Use 3 decimal places.) What are the degrees of freedom? (numerator) (denominator) (c) Find the P-value of the sample test statistic. O p-value > 0.100 O 0.050 < p-value < 0.100 O 0.025 < p-value < 0.0050 O 0.010 < p-value < 0.025 O 0.001 < p-value < 0.010 O P-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject ar fail to reject the null hypothesis? O Since the p-value is greater than the level of significance al a = 0.05, we do not reject H. O Since the p-value is less than or equal to the level of significarnce at a- 005, we reject H O Since the p-value is greater than the level of significance at a = 0.05, wc reject O Since the P valuc is less than or equal to the level of significance at a = 0.05, we do not reject. H (e) Interpret your conclusion in the context of the application. O At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal. O At the 5% level of significance there is sufficient evidence to conclude that the means are all equal. O At the 5% level of significance there is insufficient evidence to conclude that the means are all equal. O At the 5% level of significance there Is sufficient evidence to conclude that the means are not all equal. (f) Make a summary table for your ANOVA test. Source of Sum of Degrees of P Value Test MS P Type here to search 75°F Mostly sunny
Mastening Biology .
How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and
broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars)
II
III
IV
27.9
13.6
22.6
17.3
23.5
9.7
20.5
16.3
14.9
11.1
7.3
14.5
8.6
8.1
12.7
15.5
11.5
6.5
7.5
10.9
19.6
9.8
Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% level of significance.
(a) What is the level of signiflcance?
State the null and alternate hypotheses.
O Ho: = H2 = H3 = Hai H: Exactly two means are equal.
O H M = µ, = H- Hai H,: All four means are different
O H: = 2 3 - "4i H: Exactly three ineanis ate equal.
O H,: = H2 = l, = Hai H,: Not all the means are equal.
(b) Find 5STOT SSRET, ST = SSaEr + SS w (Usc 3 decimal places.)
SS TOT
SS HET=
SSw =
SS AET
and SSw and check that Ss
SSACT + SS (Usc 3 decimal places.)
!!
Find d.f. BET, d.t. w MS BET, and MS w- (Use 3 decimal places for MSarr, and MS)
BET
df BFT
RET
dr
MS BET =
MSW
Find the value of the sample / statistic. (Use 3 decimal places.)
11:04 AM
P Type here to search
75"F Mostly sunny
7/30/2021
36
Transcribed Image Text:Mastening Biology . How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars) II III IV 27.9 13.6 22.6 17.3 23.5 9.7 20.5 16.3 14.9 11.1 7.3 14.5 8.6 8.1 12.7 15.5 11.5 6.5 7.5 10.9 19.6 9.8 Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% level of significance. (a) What is the level of signiflcance? State the null and alternate hypotheses. O Ho: = H2 = H3 = Hai H: Exactly two means are equal. O H M = µ, = H- Hai H,: All four means are different O H: = 2 3 - "4i H: Exactly three ineanis ate equal. O H,: = H2 = l, = Hai H,: Not all the means are equal. (b) Find 5STOT SSRET, ST = SSaEr + SS w (Usc 3 decimal places.) SS TOT SS HET= SSw = SS AET and SSw and check that Ss SSACT + SS (Usc 3 decimal places.) !! Find d.f. BET, d.t. w MS BET, and MS w- (Use 3 decimal places for MSarr, and MS) BET df BFT RET dr MS BET = MSW Find the value of the sample / statistic. (Use 3 decimal places.) 11:04 AM P Type here to search 75"F Mostly sunny 7/30/2021 36
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 5 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman