STAT 614 ANOVA HW9
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Apr 3, 2024
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STAT 614 Applied Statistics Fall 2020 ANOVA Homework #9 1. Consider the following partial ANOVA table: Source of Variation df SS MS F Treatment * 75 25 * Error * * * Total 19 135 a. Determine the df for treatment b. Determine the df for error c. Determine the SS for error d. Determine the MS for error e. Determine the F-statistic f. Use the rejection region method (find the critical value) to test the hypothesis of equal means 2. The data in the excel file provided show the measurements of hemoglobin (g per 100 ml) in the blood of brown trout. The trout were placed at random in four different troughs. The fish food added to the troughs contained, respectively, 0, 5, 10, and 15 grams of sulfamerazine per 100 pounds of fish. The measurements were made on 10 fish randomly selected from each trough after 35 days. a. Create a summary plot of the data and comment b. Write down the null and alternative hypothesis for the test to see if there are any differences in mean hemoglobin among the different amounts of sulfamerazine added. c. Test this hypothesis using an ANOVA and α
=0.05 and draw conclusions. d. Did the outcome match what you thought would happen based on your plot, explain 3. Six observations of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content. The data (ug/g) is provided in the excel file. a. Create a summary plot of the data and comment b. Write down the null and alternative hypothesis for the test to see if there are any differences in mean thiamin content among the different types of grains. c. Test this hypothesis using an ANOVA and α
=0.05 and draw conclusions. d. Did the outcome match what you thought would happen based on your plot, explain
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Related Questions
Based on the ANOVA table given, is there enough evidence at the 0.05 level of significance to conclude that the linear relationship between the independent variables and the dependent variable is statistically significant?
Source
df
SS
MS
F
Significance F
Regression
3
1453.960807
484.653602
6.860011
0.006054
Residual
12
847.789193
70.649099
Total
15
2301.750000
A) Yes
B) No
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The dry shear strength of birch plywood bonded with different resin glues was studied with a completely randomized designed experiment. Here are the data: Glue A (102; 58; 45; 79; 68; 63; 117) Glue C (100; 102; 80; 119) Glue F (220; 243; 189; 176; 176). What is the F critical value at the 2.5% significance level
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The table below shows the numbers of bushels of barley cultivated per acre for 12 one-acre plots of land for two different strains of barley, PHT-34 and CBX-21.
PHT-34
CBX-21
43
55
49
46
47
43
38
44
47
45
45
49
50
47
46
59
46
52
46
49
45
48
43
51
Determine the minimum data value, the quartiles, and the maximum data value for the PHT-34 and CBX-21 data sets.
PHT-34
CBX-21
min
Q1
Q2
Q3
max
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Find the critical value and rejection region for the type of t-test with level of significance α and sample size n.
Right-tailed test, α=0.01, n=32
.
A.
t0=2.449;
t>2.449
B.
t0=−2.453;
t<−2.453
C.
t0=2.453;
t>2.453
D.
t0=1.309;
t>
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Use the contingency table to the right to (a) calculate the marginal frequencies, and (b) find the expected frequency for each cell in the contingency table. Assume that the variables are independent.
Rating
Size of restaurant
Excellent
Fair
Poor
Seats 100 or fewer
183
206
166
Seats over 100
180
316
151
Question content area bottom
Part 1
(a) Calculate the marginal frequencies and sample size.
Rating
Size of restaurant
Excellent
Fair
Poor
Total
Seats 100 or fewer
183
206
166
Seats over 100
180
316
151
Total
Part 2
(b) Find the expected frequency for each cell in the contingency table.
Rating
Size of restaurant
Excellent
Fair
Poor
Seats 100 or fewer
Seats over 100
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All Fresh Seafood is a wholesale fish company based on the east coast of the U.S. Catalina Offshore Products is a wholesale fish company based on the west coast of the U.S. Table #9.2.5 contains prices from both companies for specific fish types ("Seafood online," 2013) ("Buy sushi grade," 2013). Do the data provide enough evidence to show that a west coast fish wholesaler is more expensive than an east coast wholesaler? Test at the 5% level. (Show work)
Table #9.2.5: Wholesale Prices of Fish in Dollars
Fish
All Fresh Seafood Prices
Catalina Offshore Products Prices
Cod
19.99
17.99
Tilapi
6.00
13.99
Farmed Salmon
19.99
22.99
Organic Salmon
24.99
24.99
Grouper Fillet
29.99
19.99
Tuna
28.99
31.99
Swordfish
23.99
23.99
Sea Bass
32.99
23.99
Striped Bass
29.99
14.99
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Find the critical value and rejection region for the type of t-test with level of significance
α
and sample size n.
Left-tailed test,
α=0.05,
n=24
A.
t0=−1.714;
t<−1.714
B.
t0=−2.807;
t<−2.807
C.
t0=−1.711;
t<−1.711
D.
t0=1.714;
t>
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Determine the kurtosis if the data given is a sample.
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A researcher conducted a repeated measures study comparing three treatment conditions. Refer to attached images and tale to answer a to d.
Mean
Std. Deviation
N
Treatment I
1.00
1.414
5
Treatment II
5.00
2.345
5
Treatment III
6.00
1.581
5
In APA format, report the F-ratio related to the treatment effect:
Is this treatment effect significant?
What is the partial η2 value for the treatment effect?
Is this a weak, moderate, or strong effect?
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In order to determine if the average bacteria content of southern flowing streams is less than the average bacteria content of northern flowing streams, independent random samples of 28 southern flowing streams and 35 northern flowing streams were taken. Given the testing statistics below, determine if the data provides sufficient evidence to conclude that the average bacteria content of southern flowing streams is less than the average bacteria content of northern flowing streams, at the 5% significance level.
H0:μs≥μnHa:μs<μn
t0=−0.108
t0.05=−1.999
Select the correct answer below:
No; the test statistic is less than the critical value.
Yes; the test statistic is greater than the critical value.
No; the test statistic is greater than the critical value.
Yes; the test statistic is less than the critical value.
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A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.
Full data set
Carpeted
Uncarpeted
7.5
14.9
9.4
5.1
10.6
4.2
9.2
12.7
9.9
13.3
9.3
4.2
6.9
11.1
7.5
12.5
Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the
α=0.05
level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.
State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.
A.
H0:
μ1=μ2
H1:
μ1>μ2
This is the correct answer.
B.
H0:
μ1<μ2
H1:
μ1>μ2
C.
H0:
μ1=μ2
H1:
μ1≠μ2
D.
H0:
μ1=μ2
H1:
μ1<μ2
Your answer is not correct.
Determine the P-value for this hypothesis test.
P-value=nothing…
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Are yields for organic farming different from conventional farming yields? Independent random samples from method A (organic farming) and method B (conventional farming) gave the following information about yield of lima beans (in tons/acre).
Method A
1.53
1.91
1.29
1.11
1.61
1.87
1.35
1.45
1.97
1.33
2.33
Method B
1.69
2.19
1.77
2.21
1.55
1.37
2.03
1.13
1.15
1.57
1.21
1.63
b)
Compute the sample test statistic. (Use 2 decimal places.)
(c)
Find the P-value of the sample test statistic. (Use 4 decimal places.)
give directions on how to do in excel please
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The following data was calculated during a study on medical billing. Now find the critical value(s) and sketch the rejection region for this hypothesis test at a 5% significance level:
The medical billing specialist would like to test the claim that the proportion of patients with high-deductible health plans who have overdue medical bills is greater than 51%.
Sample size =35 patients with high-deductible health plans
Sample proportion =0.60
Test statistic z0=1.07
Fail to reject H0. There is NOT strong evidence to conclude that the proportion of patients with high-deductible health plans who have overdue medical bills is greater than 51%.
Fail to reject H0. There is strong evidence to conclude that the proportion of patients with high-deductible health plans who have overdue medical bills is greater than 51%.
Reject H0. There is NOT strong evidence to conclude that the proportion of patients with high-deductible health plans who have overdue medical bills is greater…
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A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference between the two processes. A summary of the findings is shown next.
Process 1
Process 2
Total
Process totals ($100s)
137
108
245
Sample size
10
10
20
Sum of squares
1,893
1,188
3,081
What is the critical value of F at the 5% level of significance?
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Refer to the ANOVA table for this regression.
Source
d.f.
SS
MS
Regression
2
578,850
289,425
Error
21
378,420
18,020
Total
23
957,270
Using Appendix F on the pictures, calculate F.05, a=0.05, F statistics, R2, and R2 adj.
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Are yields for organic farming different from conventional farming yields? Independent random samples from method A (organic farming) and method B (conventional farming) gave the following information about yield of sweet corn (in tons/acre).
Method A
6.51
7.02
6.81
7.27
6.73
6.11
6.17
5.88
6.69
7.12
5.74
6.90
Method B
7.32
7.01
6.66
6.85
5.78
6.48
5.95
6.31
6.50
5.93
6.68
Use a 5% level of significance to test the claim that there is no difference between the yield distributions.
(a) What is the level of significance?
(b) Compute the sample test statistic. (Round your answer to two decimal places.)
(c) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)
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A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population. If the researcher uses a one-tailed test with a = .01, which of the following correctly identifies the critical region?
a.
z > 2.33
b.
z > 2.58
c.
z < 2.58
d.
z < 2.33
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A researcher reports an F-ratio with dfbetween = 2 and dfwithin = 30 for an independent-measures ANOVA.
a. How many treatment conditions were compared in the experiment?
b. How many subjects participated ion the experiment?
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Use the technology of your choice to perform a residual analysis on the data.
Salary Offers. The College Placement Council conducts surveys on salary offers to candidates for degrees and publishes its findings in A Study of Beginning Offers. To study the effects of major and degree for physics and computer-science (CS) majors receiving a bachelor’s degree, a master’s degree, or a Ph.D., independent random samples of seven candidates each were obtained from the six groups under consideration. The salary data, in thousands of dollars, are given in the following table. We performed a two-way ANOVA on the data.
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In a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that evenmoderate alcohol consumption significantly slowed response time to an emergency situation in a drivingsimulation. In a similar study, researchers measured reaction time 30 minutes after participants consumed one6-ounce glass of wine. Again, they used a standardized driving simulation task for which the regular populationaverages μ = 400 msec. The distribution of reaction times is approximately normal with σ = 40. Assume that theresearcher obtained a sample mean of M = 422 for the n = 25 participants in the study.a. Are the data sufficient to conclude that the alcohol has a significant effect on reaction time? Use a two-tailed testwith α = .01.
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Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper “Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes” (Amer. J. of Clinical Nutr., 2004: 1322–1326) gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P). SubjectL 1928 2549 2825 1924 1628 2175 2114 2621 1843 2541P 2126 2885 2895 1942 1750 2184 2164 2626 2006 2627
Does the data suggest that true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g? State and test the appropriate hypotheses using a significance level of .05.
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Use the contingency table to the right to (a) calculate the marginal frequencies, and (b) find the expected frequency for each cell in the contingency table. Assume that the variables are independent.
Rating
Size of restaurant
Excellent
Fair
Poor
Seats 100 or fewer
183
206
166
Seats over 100
180
316
151
Question content area bottom
Part 1
(a) Calculate the marginal frequencies and sample size.
Rating
Size of restaurant
Excellent
Fair
Poor
Total
Seats 100 or fewer
183
206
166
555
Seats over 100
180
316
151
647
Total
363
522
317
1202
Part 2
(b) Find the expected frequency for each cell in the contingency table.
Rating
Size of restaurant
Excellent
Fair
Poor
Seats 100 or fewer
enter your response here
enter your response here
enter your response…
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Cadmium,aheavymetal,istoxictoanimals. Mushrooms,however,areabletoabsorband accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at 0.5 parts per million (ppm). M. Melgar et al. measured the cadmium levels in a random sample of the edible mushroom Boletus pinicola and published the results in a paper. Here are the data:
0.24 0.59 0.62 0.16 0.77 1.33 0.92 0.19 0.33 0.25 0.59 0.32
At the 5% significance level, do the data provide sufficient evidence to conclude that the mean cadmium level in Boletus pinicola mushrooms is greater than the government’s recommended level of 0.5 ppm? Assume that the population standard deviation of cadmium levels in Boletus pinicola mushrooms is 0.37 ppm (Note: The sum of the data is 6.31 ppm.)
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- Based on the ANOVA table given, is there enough evidence at the 0.05 level of significance to conclude that the linear relationship between the independent variables and the dependent variable is statistically significant? Source df SS MS F Significance F Regression 3 1453.960807 484.653602 6.860011 0.006054 Residual 12 847.789193 70.649099 Total 15 2301.750000 A) Yes B) Noarrow_forwardThe dry shear strength of birch plywood bonded with different resin glues was studied with a completely randomized designed experiment. Here are the data: Glue A (102; 58; 45; 79; 68; 63; 117) Glue C (100; 102; 80; 119) Glue F (220; 243; 189; 176; 176). What is the F critical value at the 2.5% significance levelarrow_forwardThe table below shows the numbers of bushels of barley cultivated per acre for 12 one-acre plots of land for two different strains of barley, PHT-34 and CBX-21. PHT-34 CBX-21 43 55 49 46 47 43 38 44 47 45 45 49 50 47 46 59 46 52 46 49 45 48 43 51 Determine the minimum data value, the quartiles, and the maximum data value for the PHT-34 and CBX-21 data sets. PHT-34 CBX-21 min Q1 Q2 Q3 maxarrow_forward
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- Find the critical value and rejection region for the type of t-test with level of significance α and sample size n. Left-tailed test, α=0.05, n=24 A. t0=−1.714; t<−1.714 B. t0=−2.807; t<−2.807 C. t0=−1.711; t<−1.711 D. t0=1.714; t>arrow_forwardDetermine the kurtosis if the data given is a sample.arrow_forwardA researcher conducted a repeated measures study comparing three treatment conditions. Refer to attached images and tale to answer a to d. Mean Std. Deviation N Treatment I 1.00 1.414 5 Treatment II 5.00 2.345 5 Treatment III 6.00 1.581 5 In APA format, report the F-ratio related to the treatment effect: Is this treatment effect significant? What is the partial η2 value for the treatment effect? Is this a weak, moderate, or strong effect?arrow_forward
- In order to determine if the average bacteria content of southern flowing streams is less than the average bacteria content of northern flowing streams, independent random samples of 28 southern flowing streams and 35 northern flowing streams were taken. Given the testing statistics below, determine if the data provides sufficient evidence to conclude that the average bacteria content of southern flowing streams is less than the average bacteria content of northern flowing streams, at the 5% significance level. H0:μs≥μnHa:μs<μn t0=−0.108 t0.05=−1.999 Select the correct answer below: No; the test statistic is less than the critical value. Yes; the test statistic is greater than the critical value. No; the test statistic is greater than the critical value. Yes; the test statistic is less than the critical value.arrow_forwardA researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms. Full data set Carpeted Uncarpeted 7.5 14.9 9.4 5.1 10.6 4.2 9.2 12.7 9.9 13.3 9.3 4.2 6.9 11.1 7.5 12.5 Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the α=0.05 level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers. State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms. A. H0: μ1=μ2 H1: μ1>μ2 This is the correct answer. B. H0: μ1<μ2 H1: μ1>μ2 C. H0: μ1=μ2 H1: μ1≠μ2 D. H0: μ1=μ2 H1: μ1<μ2 Your answer is not correct. Determine the P-value for this hypothesis test. P-value=nothing…arrow_forwardAre yields for organic farming different from conventional farming yields? Independent random samples from method A (organic farming) and method B (conventional farming) gave the following information about yield of lima beans (in tons/acre). Method A 1.53 1.91 1.29 1.11 1.61 1.87 1.35 1.45 1.97 1.33 2.33 Method B 1.69 2.19 1.77 2.21 1.55 1.37 2.03 1.13 1.15 1.57 1.21 1.63 b) Compute the sample test statistic. (Use 2 decimal places.) (c) Find the P-value of the sample test statistic. (Use 4 decimal places.) give directions on how to do in excel pleasearrow_forward
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