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
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
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
Related questions
Topic Video
Question
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
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
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 5 images
Knowledge Booster
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.Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning