12 points Six samples of each of four types of cereal grain

(12 points) Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamine content (g/g). Use the graindata.csv data set and R code from Data Sets and Code to analyze whether there is evidence that the mean thiamine content differs among the grain types.

a. (3 points) Plot and paste a side-by-side box plot that compares the thiamine content among the grain types. From the side-by-side box plot does there look to be a difference in the average thiamine content among grains? Explain which grains look to be different/same.

b. Perform a Single Factor ANOVA to test whether there is evidence that the mean thiamine content differs among the grain types.

a. (2 points) State the null and alternative hypotheses.

b. (4 points) Paste ANOVA test output from R. Use the F statistic and p-value from the output to make a conclusion about the test. Use a significance level of 0.05. Include context from the problem.

c. (3 points) Perform a Tukey’s Multiple Comparison procedure. Paste the R output. Are there any individual comparisons that are significant at the 0.05 significance level? If so, state which ones and give the estimated difference.

data of ST314 Student Information Survey(2).

Data of graindata:

GIVEN CODE:

# Download the ST314 Student Survey Data.

# Save it where you will remember.

# Upload Data Set into R.

# Highlight and Run the line below. Select the data file from browse window.

# The data has now been named \"st314data\"

st314data = read.csv(file.choose(), header = TRUE)

# Take a look at st314data. By running the name.

st314data

# Part 1 OPTIONAL.

# This code will recreate the information provided in the Data Analysis Part 1

# Creates a side by side boxplot

boxplot(st314data$CloseFriends~st314data$Profile, horizontal = TRUE,

main = \"Number of Reported Close Friends

among ST314 Summer Students w/

or w/out a Social Networking Profile\", col = \"aquamarine\" ,

xlab = \"Number of Close Friends\",

axes = FALSE)

axis(1, at = seq(0,50,5))

axis(2, at = c(1,2), labels = c(\"No Profile\", \"Profile\"))

# Performs a Pooled Two Sample T Test assumes population variances are the same.

t.test(st314data$CloseFriends~st314data$Profile, var.equal = TRUE)

# Get Summary Statistics for each group

Profile.Average = mean(st314data$CloseFriends[st314data$Profile==\"TRUE\"])

Profile.Average

Profile.sd = sd(st314data$CloseFriends[st314data$Profile==\"TRUE\"])

Profile.sd

Profile.n = length(st314data$CloseFriends[st314data$Profile==\"TRUE\"])

Profile.n

NOProfile.Average = mean(st314data$CloseFriends[st314data$Profile==\"FALSE\"])

NOProfile.Average

NOProfile.sd = sd(st314data$CloseFriends[st314data$Profile==\"FALSE\"])

NOProfile.sd

NOProfile.n = length(st314data$CloseFriends[st314data$Profile==\"FALSE\"])

NOProfile.n

# Part 2g

# Perform a Welch\'s Two Sample T Test

t.test(st314data$CloseFriends~st314data$Profile)

# Part 3

# Download and Save the grain data set.

# Upload Data Set into R.

# Highlight and Run the line below. Select the data file from browse window.

# The data has now been named \"gdata\"

gdata = read.csv(file.choose(), header = TRUE)

# Take a look at gdata. By running the name.

gdata

# Create a boxplot of thiamin content vs grain type.

boxplot(gdata$thiamine~gdata$grain, col = \"yellow\", main = \"Thiamine Content among Four Types of Cereal Grain\")

# Perform a Single-Factor ANOVA to compare mean thiamine of the four grain types.

mod = aov(gdata$thiamine~gdata$grain)

summary(mod)

# If the test is significant from the Single Factor ANOVA, perform a multiple comparisons procedure.

TukeyHSD(mod)

SchoolWorkHours	CreditHours	SchoolMaterialsDollars	TermstoGrad	Height	Job	Salary	CloseFriends	Activity	TextMessages	Profile	SocialTime	WeightDesire	DayBorn	Gender	FemalePresident	GradSchool	SubjectPreferred
14	6	100	9	62	2	57000	3	60	60	TRUE	10	Maintain	Wednesday	Female	FALSE	FALSE	Math
12	3	75	6	64	4	70000	3	60	100	TRUE	30	Maintain	Sunday	Female	TRUE	TRUE	Math
8	3	900	2	66	8	85000	3	120	30	TRUE	30	Maintain	Friday	Female	TRUE	TRUE	Math
24	7	100	8	63	1	50000	3	30	28	FALSE	0	Increase	Thursday	Female	TRUE	FALSE	Math
10	3	85	2	62	8	60000	11	300	26	TRUE	20	Maintain	Saturday	Female	TRUE	TRUE	Math
10	12	100	8	60	2	20000	5	60	60	TRUE	100	Decrease	Tuesday	Female	TRUE	TRUE	Math
20	10	200	2	49	3	80000	5	75	60	TRUE	15	Maintain	Monday	Female	TRUE	TRUE	Math
14	6	130	9	68.5	4	55000	15	30	34	TRUE	60	Decrease	Wednesday	Female	TRUE	FALSE	Writing
9	3	80	10	69	1	55000	10	30	55	TRUE	60	Decrease	Friday	Female	TRUE	TRUE	Math
10	6	100	8	72	6	70000	4	45	75	TRUE	45	Maintain	Tuesday	Female	TRUE	FALSE	Math
8	6	150	12	62	3	60000	4	60	20	TRUE	60	Maintain	Monday	Female	TRUE	FALSE	Math
10	6	0	3	78	1	50000	2	100	100	TRUE	120	Decrease	Friday	Female	TRUE	TRUE	Math
4	6	200	7	63	1	50000	5	60	500	TRUE	300	Decrease	Sunday	Female	TRUE	TRUE	Math
12	15	400	3	62	7	70000	3	90	100	TRUE	45	Decrease	Tuesday	Female	TRUE	TRUE	Math
3	3	80	2	64	3	55000	4	60	30	TRUE	30	Decrease	Friday	Female	TRUE	TRUE	Math
3	3	75	8	65	0	40000	15	30	10	TRUE	30	Decrease	Friday	Male	TRUE	TRUE	Math
2	7	200	8	76	3	60000	5	60	30	TRUE	120	Decrease	Thursday	Male	TRUE	FALSE	Math
18	8	0	4	72	2	50000	6	30	10	TRUE	5	Increase	Wednesday	Male	TRUE	FALSE	Math
6.5	3	1000	5	70	5	50000	8	60	5	FALSE	0	Increase	Wednesday	Male	TRUE	TRUE	Math
3	12	100	1	69	1	50000	2	120	100	TRUE	4	Maintain	Sunday	Male	TRUE	FALSE	Math
24	12	200	8	180	1	58000	6	120	60	TRUE	60	Decrease	Wednesday	Male	TRUE	TRUE	Math
20	6	75	1	73	4	65000	4	45	100	TRUE	60	Decrease	Monday	Male	FALSE	FALSE	Math
4	3	0	8	74	3	60000	8	30	100	TRUE	20	Decrease	Monday	Male	TRUE	FALSE	Math
7	8	200	14	71	1	80000	2	100	10	TRUE	360	Maintain	Monday	Male	TRUE	TRUE	Writing
15	3	30	4	74	8	70000	8	30	62	TRUE	5	Decrease	Thursday	Male	TRUE	FALSE	Math
21	9	3000	8	67	2	70000	17	60	12	TRUE	30	Decrease	Wednesday	Male	TRUE	TRUE	Math
25	13	400	8	71	1	65000	5	190	15	TRUE	45	Increase	Thursday	Male	TRUE	FALSE	Math
50	16	300	2	75	5	95000	15	30	400	TRUE	180	Decrease	Tuesday	Male	TRUE	FALSE	Math
8	3	200	4	70	6	70000	6	60	500	TRUE	300	Increase	Sunday	Male	TRUE	TRUE	Math
22	8	2000	8	69	2	40000	12	60	20	TRUE	2	Maintain	Thursday	Male	FALSE	TRUE	Math
6	10	150	8	69	1	60000	3	60	10	TRUE	60	Maintain	Saturday	Male	TRUE	FALSE	Math
24	11	130	7	72	18	55000	5	30	10	TRUE	60	Maintain	Saturday	Male	TRUE	FALSE	Math
20	3	1000	1	69	4	40000	1	65	4	TRUE	80	Decrease	Tuesday	Male	FALSE	FALSE	Math
5	7	150	2	72	8	110000	9	60	200	TRUE	15	Maintain	Wednesday	Male	TRUE	FALSE	Writing
3	3	0	8	73	2	70000	5	30	30	TRUE	60	Decrease	Tuesday	Male	TRUE	TRUE	Math
25	10	300	1	72	3	70000	4	30	10	TRUE	60	Maintain	Thursday	Male	TRUE	TRUE	Math
2	3	70	3	70	1	30000	4	0	8	TRUE	0	Increase	Wednesday	Male	TRUE	FALSE	Math
3.5	8	200	4	72	2	45000	3	45	3	TRUE	0	Increase	Saturday	Male	TRUE	FALSE	Writing
6	6	200	7	72	0	30000	3	15	3	TRUE	300	Increase	Tuesday	Male	FALSE	TRUE	Math
10	13	250	10	70	2	50000	3	70	20	TRUE	30	Maintain	Thursday	Male	TRUE	FALSE	Math
5	4	150	8	75	2	70000	10	40	20	TRUE	45	Decrease	Monday	Male	TRUE	TRUE	Math
20	7	160	7	71	4	70000	10	0	20	TRUE	20	Maintain	Tuesday	Male	TRUE	TRUE	Writing
45	19	175	4	75	7	60000	9	45	50	TRUE	30	Increase	Thursday	Male	TRUE	TRUE	Math
8	10	250	6	72	5	60000	10	120	50	TRUE	75	Increase	Wednesday	Male	FALSE	FALSE	Math
20	3	100	6	71.5	0	77720	5	60	15	TRUE	90	Increase	Tuesday	Male	FALSE	TRUE	Math
30	14	600	13	73	2	79000	12	30	500	TRUE	60	Decrease	Tuesday	Male	TRUE	FALSE	Math
30	12	600	4	69	10	70000	4	30	20	TRUE	30	Maintain	Tuesday	Male	TRUE	FALSE	Math
4	6	100	8	73	13	50000	1	20	0	TRUE	30	Decrease	Sunday	Male	TRUE	TRUE	Math
10	4	0	2	76	3	35000	2	60	5	TRUE	60	Decrease	Wednesday	Male	TRUE	FALSE	Writing
9	3	80	4	66	6	50000	5	90	12	FALSE	0	Decrease	Thursday	Male	TRUE	FALSE	Math
10	3	0	7	72	1	35000	5	60	10	TRUE	40	Maintain	Sunday	Male	TRUE	FALSE	Math
10	6	75	8	65	0	20000	50	180	100	FALSE	0	Decrease	Wednesday	Male	TRUE	TRUE	Writing
6	3	200	6	68	3	63000	1	120	10	TRUE	10	Decrease	Tuesday	Male	TRUE	FALSE	Math
4	3	200	8	69	4	75000	4	300	250	TRUE	60	Decrease	Wednesday	Male	TRUE	TRUE	Math
6	9	300	8	5.6	0	58000	1	50	23	TRUE	300	Decrease	Sunday	Male	TRUE	TRUE	Math
16	12	100	8	72	4	40000	3	20	18	TRUE	120	Decrease	Thursday	Male	TRUE	TRUE	Writing
10	3	75	10	67	3	80000	4	120	2	TRUE	120	Increase	Tuesday	Male	TRUE	TRUE	Math
5	3	1350	9	70	12	75000	2	510	11	FALSE	0	Maintain	Saturday	Male	TRUE	FALSE	Math
20	10	150	8	71	3	40000	3	60	10	TRUE	30	Increase	Tuesday	Male	FALSE	TRUE	Math
15	4	133	8	64.5	0	40000	8	15	56	TRUE	30	Increase	Wednesday	Male	TRUE	TRUE	Math
4	13	300	8	67	3	80000	2	70	150	TRUE	15	Maintain	Monday	Male	TRUE	TRUE	Math

Solution

Using Minitab the oneway ANOVA code is,

Minitab output is,