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.

1.     (3 points) Answer the one question in the Assignment 2 survey as accurately as you can: How much did you spend on eating out over the past 7 days (food and non-alcoholic beverages only)? Complete this survey by 11 PM on Sunday of Week 2.

The data collected from the class will be posted in the food.csv data set on Canvas on Monday of Week 3.

2    (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.)

      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?)

Data Set:

amount
75
70
50
59
130
65
20
50
50
100
25
46.18
7
20
25
10
60
35
25
15
180
280
12.66
5
40
100
102.64
25
14.57
15
40
70
63
20
48
17.12
30
50
40
70
30
70
10
0
85
34
100
20
0
100
20

Answer 1

Let X be the random variable that denotes the spending of past 7 days or 1 week.

We assume X~N(u,a²).

Here we have a sample of size 51 from X

And here we want to estiamte u

We know xbar=sample mean is the best estimate so use the R code

x=c(75,70,50,59,130,65,20,50,50,100,25,46.18,7,20,25,10,60,35,25,15,180,280,12.66,5,40,100,102.64,25,14.57,15,40,70,63,20,48,17.12,30,50,40,70,30,70,10,0,85,34,100,20,0,100,20)
x
xbar=mean(x)

and get xbar =51.55

so estimated average spending in one week is 51.55 so estimated spemding for 32 weeks is 32*51.55=1649.6

Get the descriptive statistics by r code

summary(x)

sd(x) # will give the standard deviation=48.9341

Result is

summary(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 20.00 40.00 51.55 70.00 280.00

And draw an histogram of the data byb the R code

If we do the test that H₀:u=51.55 ag H₁: u=! 51.55

then a 95 % vconfidence interval for u will be provided

R code

t.test(x,mu=55.51,alternative="two.sided")

And the result is

One Sample t-test

data: x
t = -0.57758, df = 50, p-value = 0.5661
alternative hypothesis: true mean is not equal to 55.51
95 percent confidence interval:
37.78941 65.31529
sample estimates:
mean of x
51.55235

so a 95 percent confidence interval:
(37.78941, 65.31529)

To check the validity we need to check the normaality of the data so we draw the normal probability plot for the data. R code

qqnorm(x)

Result is

However the data doesnt seem to come from a normal distn. and from the histogram of the data it semmed that it may come from an exponential distn alternatively we could have started with an exponential distn and carry out our analysis.