Question

Brett is a high school senior and is planning on attending a state university next year. Brett will be on a meal plan in his dorm, but his father knows that he will eat out every once in awhile. Brett’s father wondered just how much college students spent on eating out each week so he could incorporate this into Brett’s college budget. To determine the average amount spent on eating out each week, Brett’s father is seeking help from the ST 352 online class by conducting a survey.

(12 points) Analyze the data in the food.csv data set in a proper way to answer the question of interest, "How much should Brett's father budget for the year for Brett to eat out?" (Assume Brett will be at school for 32 weeks during the year.) (R tutorial 2 may be helpful in answering this question.) 2 Write a short report that includes at a minimum (but not necessarily in this order) An answer to the question supported with a confidence interval Descriptive statistics and an appropriate graphical display of the sample data What method you used to obtain the confidence interval and why (include a check of the conditions to use that particular method, which may require another graphical display) A discussion of whether you feel it is reasonable to use the results of this study to make conclusions about how much Brett will spend on eating out. (What are we assuming about Brett if you do?)

amount
60
40
110
53
20
65
30
18
25
30
8
50
100
78
8.33
75
50
40
50
36.3
8.97
65
149
55
50
40
9
40.21
80
227
30
55
50
100
40
80
15
75
14.52
40
0
20
30
19
25
9.5
160
11.08
50
50
67
140
90
25
25
30
9
30
0
100
30
25
30
48.34
98
100
35
17
25
20
20
50
20
50
0
30
30.62
20
50
62

Answer 1

a.

Output:

One Sample t-test

data: G1
t = 10.864, df = 79, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
39.02063 56.52612
sample estimates:
mean of x
47.77338
Ans: 95% confidence interval ( 39.02063, 56.52612).

b. amount
Min. : 0.00
1st Qu.: 20.00
Median : 40.00
Mean : 47.77
3rd Qu.: 60.50
Max. :227.00

Standard deviation: 39.33127

skewness: 1.888104

kurtosis: 7.867967

Hence the distribution is positively skewed.

c. For constructing confidence interval we assume normality. This can be verified by drawing QQ plot.

From the above plot is observed that most of the data points are closed to the reference line hence normality assumption valid.

So from the confidence interval his father is 95% confident that the average amount spent on eating out each week lies between 39.02hr. to 56.53 hr.

R code:

G=read.csv(choose.files(filters=Filters["All",]))
G1=data.frame(GD)
G1
t.test(G1,conf.level = 0.95)
summary(G1)
sd(G1[,1])
library(moments)
skewness(G1[,1])
kurtosis(G1[,1])
hist(G1[,1],breaks=7,xlab="Class boundary",main="Histogram of Amount")
qqnorm(G1[,1],lwd=2, type="p",col=1, main="Normal Q-Q plot of Amount data")
qqline(G1[,1],lwd=2, type="l",col=2)