Elementary probability and statistics question

Ramapo College

Elementary Probability and Statistics Summer 2020

Test 1 Time Allowed: 120 Minutes

NOTE: Show your work and the formulas you use for each problem.

Your Name:

True/False, circle T or F (2 Points Each):

1. Number of hours per day using internet is an example of nominal data. T F

2. Median is always smaller than the 2nd quartile. T F

3. Histogram is a good chart to summarize qualitative data. T F

4. For the same data set, standard deviation value always equals variance value. T F

5. Mode is the best measure to summarize quantitative data. T F

Multiple choice questions. Please circle the correct answer for each. (2 points each)

1. Which of the following is most likely a sample as opposed to a population?

a. All customers of a bank

b. Students in a given university

c. Every fifth student to arrive at the book store on your campus

d. Registered voters in the State of Michigan

2. Data

a.	is always numeric.
b.	is always nonnumeric.
c.	Can be numeric or nonnumeric.
d.	None of the above.

3. All calculations are permitted on what type of data?

a.	Interval data
b.	Nominal data
c.	Ordinal data
d.	All of these choices are true.

4. Qualitative data

a.	must be numeric.
b.	must be nonnumeric.
c.	cannot be numeric.
d.	may be either numeric or nonnumeric.

5. The pie chart is an appropriate chart for

a.	numerical data only.
b.	ratio scale data only.
c.	categorical data.
d.	Interval data only.

1- (10 Points)

A survey of students was conducted to determine how they rate the quality of on-line classes. Students were asked to rate the overall quality as Excellent (E), Very Good (V), Good (G) and Poor (P). The following data were obtained:

E	G	G	V	P	P	V	V	E	V
P	E	G	G	V	V	P	P	V	E
P	V	G	G	G	G	E	V	P	G
V	V	V	V	P	P	G	G	E	V

a) What percentage of students rated the quality as Very Good?

b) Construct a bar graph of this data and provide required descriptive information for this graph.

2-(15 Points)

The grades on a calculus exam for a sample of 40 students are as follows:

63 74 42 65 51 54 34 56 68 57

62 64 76 67 79 61 81 77 59 38

84 68 71 94 71 86 69 75 91 55

48 82 83 54 79 62 68 58 41 47

a) Construct a frequency distribution. Construct a frequency histogram for these data.

b) Construct a cumulative frequency and graph it (Ogive).

3- (15 Points)

Using the data in problem 1 above,

a) Calculate the required measurements for box-plots (include the lower and upper fences) and construct the box-plots.

b) Calculate the interquartile range.

4- (15 Points)

The mean income of a group of people is $500/week, and the standard deviation is $40. Using the Empirical Rule, find the percent of the incomes

a) Less than $580.

b) between $540 and $580.

c) Higher than $620.

5- (10 Points)

Find the Z-score for the following data and identify outliers if any?

99, 97, 102, 112

5- (15 Points)

Consider the following sample:

x	12	6	8	5
y	22	14	12	14

a) Show the scatter diagram.

b) Calculate the linear correlataion coefficient, and comment on the relationship between x and y.

c) Find the least squares line. Find the value of y, if x is 15.