Question

The
following data set contains the college GPA of a sample of ten
randomly selected UWG professors:

1.8, 2.1, 2.3, 2.5, 2.6, 3.2, 3.4, 3.7, 3.9, 4

A.) Construct a normal probability plot of the data set. Do
the GPA’s appear to be normally distributed? Yes or No.

B.) Find the critical t value that corresponds to a 90%
confidence level for the data rounded to 2 decimal places.

C.) Construct a 90% confidence interval for the mean GPA of
the professors, round answers to 2 decimal places.

Answer #1

A) By using R software we can construct the normal probability plot of the data set.

First, enter data into R software.

R codes and output.

data<-c(1.8,2.1,2.3,2.5,2.6,3.2,3.4,3.7,3.9,4)

qqnorm(data)

Yes, the GPA’s appear to be normally distributed.

B)

Sample size = n = 10

Degrees of freedom = n - 1 = 10 - 1 = 9

Level of significance = 0.10

**Critical value = 1.83 ** ( Using t
table)

C) We have to construct a 90% confidence interval for the mean GPA of the professors.

Sample mean = = 2.95

Standard deviation = s = 0.7906

Formula is

Here E is a margin of error.

So confidence interval is ( 2.95 - 0.4575 , 2.95 + 0.4575) =
> **( 2.49 , 3.41)**

The grade point averages (GPA) of 18 randomly selected college
students are used to estimate the mean GPA of the college students.
The GPAs from the sample are as follows: 2.3 3.3 2.6 1.8 0.9 3.1
4.0 0.7 3.1 2.3 2.0 3.1 3.4 1.3 2.6 2.6 3.7 2.2
a- Would it be justified if the standard normal distribution is
used to construct the confidence interval? Explain.
b-If the population is assumed to be normally distributed,
construct a 98% confidence interval...

The grade point averages (GPA) for 12 randomly selected college
students are shown below. Complete parts (a) through (c)
below.
Assume the population is normally distributed.
2.3
3.3
2.7
1.8
0.9
4
2.2
1.4
3.9
0.5
2.3
3.2
(a) Find the sample mean= (Round to two decimal
places as needed.)
(b) Find sample Standard deviation= (Round to two
decimal places as needed.)
(C) construct 90% confidence interval= _ , _
(Round to two decimal places as needed.)

Data shows the times for carrying out a blood test at
Rivervalley Labs
Using Excel Plot a histogram of the data. What type of
distribution does the data appear to follow?
Construct and interpret the 95% confidence interval for the
population mean time for carrying out a blood test. Assume that the
population standard deviation is unknown.
Times for blood tests (minutes)
2.5
4.9
3.6
4.3
1.9
3.4
3.2
4.0
3.1
3.6
3.9
4.4
3.9
3.1
2.7
3.5
3.6
3.7...

Estimate: GPA = β0 + β1GRE + ε, where GRE is a student’s score
on the math portion of the Graduate Record Examination (GRE) score
and GPA is the student’s grade point average in graduate
school.
GPA
GRE
3.9
690
3.2
740
3.1
740
2.7
650
2.5
700
2.9
640
2.7
710
2.9
700
2.1
760
2.3
670
3.6
750
2.5
700
3.4
650
3.9
690
3.3
700
2.7
680
3.8
660
2.6
660
3.9
710
3.8
760
3
690...

The grade point averages (GPA) for 12 randomly selected college
students are shown on the right. Complete parts (a) through (c)
below. Assume the population is normally distributed.
2.3 3.4 2.8 1.8 0.9 4.0 2.5 1.1 3.8 0.5 2.2 3.2
(a) Find the sample mean. x overbarequals =
(Round to two decimal places as needed.)
(b) Find the sample standard deviation. sequals =
(Round to two decimal places as needed.)
(c) Construct a 95% confidence interval for the population
mean...

Please explain step by step.
The following data represents the GPA of a sample of 15 students
enrolled in a history class.
3.4, 3.9, 4.0, 2.8, 3.5, 2.6, 3.2, 3.6, 1.9, 2.1, 2.0, 3.3, 2.4,
1.8, 3.2
(a) Find the first quartile. Do not include the median in the
calculations.
Answer: __________________
(b) Find the third quartile. Do not include the median in the
calculations.
Answer: __________________
(c) Find the mean.(Round to 2 decimal places.)
Answer: __________________
(d) Find the...

–Construct a reasonable frequency distribution of High School
GPA (HSGPA)
–Construct a histogram
–Present the frequency distribution and histogram
There are a total of 188 HS student GPAs.
1.6, 2, 2.1, 2.1, 2.2, 2.2, 2.2, 2.4, 2.4, 2.5, 2.5, 2.5, 2.5,
2.5, 2.6, 2.7, 2.75, 2.75, 2.75, 2.75, 2.75, 2.8, 2.8, 2.8, 2.9,
2.9, 2.9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3.1, 3.1, 3.1, 3.2, 3.2, 3.2,...

A researcher wants to know if the clothes a woman wears is a
factor in her GPA. The table below shows data that was collected
from a survey.
Shorts
Dress
Jeans
Skirt
3.9
2.6
2.7
3.4
2.1
2.6
1.8
3.5
2.4
2.3
3
3.5
2
2.1
4
3.8
3.7
2.6
2.3
3.2
2.5
2.6
2.8
3.5
3.6
1.9
2.9
2.9
2.2
2.3
2.2
2.1
2.7
3.5
Assume that all distributions are normal, the four population
standard deviations are all the...

The data set below is a random sample of the weights (in oz.)
of 15 donuts. From this, can we conclude with 95% confidence that
the mean weight of a donut is greater than 2 ounces? Justify your
answer.
2.3
2.6
2.0
2.4
1.8
3.1
2.2
2.5
1.7
2.1
1.4
2.0
1.5
2.6 2.3

12. ANALYSIS
OF VARIANCE
The average of grade
point averages (GPAs) of college courses in a specific major is a
measure of difficulty of the major. An educator wishes to conduct a
study to find out whether the difficulty levels of different majors
are the same. For such a study, a random sample of major grade
point averages (GPA) of 8 graduating seniors at a large university
is selected for each of the four majors mathematics, English,
Education, and Biology...

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