Question

1. GPA Versus Seating Location. A professor wanted to know whether there was a difference in students’ grade point averages (GPA) depending on whether they sit in the front half of the classroom versus the back half of the classroom. In a previous semester, a random sample of students was selected from the front of a classroom and another random sample was selected from the back of a classroom and each student’s current GPA was recorded. The data provided in StatCrunch represent the GPAs from each random sample. At the 0.01 significance level, can the professor conclude from these data that the mean GPA for front sitters is different from than back sitters?  
2. Front GPA   Back GPA
3. 4.1   4.06
   4   4
   4   3.92
   3.92   3.7
   3.9   3.6
   3.9   3.5
   3.89   3.5
   3.876   3.43
   3.8   3.4
   3.8   3.4
   3.71   3.4
   3.7   3.25
   3.7   3.2
   3.7   3.2
   3.6   3.2
   3.54   3.1
   3.5   3.05
   3.5   3
   3.5   3
   3.5   3
   3.44   3
   3.4   3
   3.4   3
   3.4   3
   3.39   2.95
   3.33   2.94
   3.3   2.9
   3.26   2.9
   3.26   2.9
   3.25   2.87
   3.24   2.84
   3.22   2.8
   3.21   2.8
   3.11   2.8
   3.1   2.7
   3   2.67
   3   2.58
   3   2.5
   3   2.5
   3   2.5
   3   2.5
   2.9   2.46
   2.8   2.4
   2.67   2.1
   2.62   2.06
   2.5   2.04
   2.44   2
   2.05   ""
   2 ""
   2 ""
   1.96   ""
   1.92   ""

1. What is (are) the parameter(s) of interest? Choose one of the following symbols (m (the mean of one sample); m_D(the mean difference from a paired (dependent) samples);m₁ - m₂ (the mean difference of two independent samples) and describe the parameter in context of this question in one sentence.

2. Depending on your answer to part (i), construct one or two relative frequency histograms. Remember to properly title and label the graph(s). Copy and paste the graph(s) into your document.

3. Describe the shape of the histogram(s) in one sentence.

4. Depending on your answer to part (i), construct one or two boxplots and copy and paste these graphs into your document.

5. Does the boxplot (or do the boxplots) show any outliers? Answer this question in one sentence and identify any outliers if they are present.

6. Considering your answers to parts (iii) and (v), is inference appropriate in this case? Why or why not? Defend your answer using the graphs in two to three sentences.

2. GMU Health Center Waiting Time. During the flu season, it is known that the waiting time at the GMU Health Center can be extreme. A statistics student wanted to test her claim that the wait time was greater than 100 minutes. She took a random sample of wait times during the flu season and recorded them in StatCrunch.
3. Waiting Time
   104.97
   120.72
   130.76
   137.39
   96.65
   240.49
   95.46
   107.98
   103.07
   116.83
   87.44
   114.05
   109.56
   120.6
   126.41
   135.78
   97.66
   19.75
   216.87
   114.29
   113.92

1. What is (are) the parameter(s) of interest? Choose one of the following symbols (m (the mean of one sample); m_D(the mean difference of two paired (dependent) samples);m₁ - m₂ (the mean difference of two independent samples) and describe the parameter in context of this question in one sentence.

2. Depending on your answer to part (i), construct one or two relative frequency histograms. Remember to properly title and label the graph(s). Copy and paste the graph(s) into your document.

3. Describe the shape of the histogram(s) in one sentence.

4. Depending on your answer to part (i), construct one or two boxplots and copy and paste these graphs into your document.

5. Does the boxplot (or do the boxplots) show any outliers? Answer this question in one sentence and identify any outliers if they are present.

6. Considering the answers provided in parts (iii) and (v), is inference appropriate in this case? Why or why not? Defend your answer using the graphs in two to three sentences.

Answer 1

A

i) Statistics

Variable	N	N*	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum
Front GPA	52	0	3.2367	0.0792	0.5712	1.9200	3.0000	3.3150	3.7000	4.1000
Back GPA	47	5	2.9706	0.0713	0.4886	2.0000	2.6700	3.0000	3.2500	4.0600

m1 = 3.2367 (front GPA)

m2 = 2.9706 (Back GPA)

m1-m2 = 0.2661

With the sample data, it seems that there is a difference between the mean of GPA because of seating arrangement, but we need to identify if the difference is real or just due to sampling variation

ii) Histogram of both data points

iii) The shape of both the graphs tends to follow approximate normal distribution

iv) Box plot for the GPA

v) One outlier (point away 1.5 IQR from the median) is identified in Front GPA

vi) Because of the outliers, there is a deviation from the normality (seen in the Boxplot)

B

i) Statistics

Variable	N	N*	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum
Waiting Time	21	0	119.55	9.54	43.73	19.75	100.36	114.05	128.58	240.49

Mean (m1) = 119.5

Hypotheised mean (mo) = 100

mo - m1 = -19.5

With the sample data, it seems that there is a difference between the mean of waiting time in flu season is there, but we need to identify if the difference is real or just due to sampling variation

ii) Histogram

iii) The histogram tends to follow normal distribution (a little deviation due to presence of outliers)

iv) Box plot

v) There are a few outliers present in the data

vi) Because of the outliers, there is a deviation from the normality (seen in the Boxplot)