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STA 100 Exam 1: Statistics Problem Solving - Prof. William Thistleton, Exams of Data Analysis & Statistical Methods

State University of New York Polytechnic - Utica-RomeData Analysis & Statistical Methods
Prof. William Thistleton

The solutions manual for exam 1 of statistics 100 (sta 100). It includes problems on finding the five number summary, inter-quartile range, evaluating expressions, calculating probabilities, variances, and creating a histogram. Students are expected to consult their textbook and classroom notes for assistance.

Typology: Exams

Pre 2010

Uploaded on 08/09/2009

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STA 100 Exam 1 October 11, 2006
Prof. Thistleton
1. Given the data below, find the 5 number summary and the inter-quartile range, IQR.
108 96 94 95 77
96 101 104 121 94
109 111 114 85 103
2. Evaluate the following expressions:
P5
i=2(i2)10 P5 10C5
3. A population has a mean µ= 80 and a standard deviation σ= 20. Using Chebyshev’s
Theorem, make a statement about the proportion of the population between 40 and 120.
1
pf3
pf4
pf5

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STA 100 Exam 1 October 11, 2006 Prof. Thistleton

  1. Given the data below, find the 5 number summary and the inter-quartile range, IQR.

108 96 94 95 77 96 101 104 121 94 109 111 114 85 103

  1. Evaluate the following expressions:

∑ 5 i=2(i

2 ) 10 P 5 10 C 5

  1. A population has a mean μ = 80 and a standard deviation σ = 20. Using Chebyshev’s Theorem, make a statement about the proportion of the population between 40 and 120.
  1. Suppose there are 200 students in a large statistics lecture. 40% of these students are freshmen. 50% of these students are Business majors. There are exactly 30 students who are freshmen and Business majors.

(a) Fill in the following table.

Business NOT Business Freshman NOT Freshman total =

(b) What is the probability that a randomly selected student is not a Business major?

(c) If you know that a randomly selected student is a Business major, what is the probability that they are a freshman?

(d) If you know that a randomly selected student is not a freshman, what is the probability that they are a Business major?

  1. Calculate the variance of the data points. Use the computational formula and show all your work.

xi 1 1 2 2 4 3 5

  1. You will pick 2 marbles from a bag which has 3 red and 5 green marbles.

(a) What is the probability of picking 0, 1, or 2 green marbles if you keep the marbles out as you pick? (sampling without replacement)

(b) What is the probability of picking 0, 1, or 2 green marbles if you replace the each marble and shake the bag before you pick the next one? (sampling with replacement)

  1. (Extra Credit +10 ) A test is designed to determine whether a patient has the flu or not. The specificity of this test is 0.97 and its sensitivity is 0.96. Suppose 30% of students at a university have the flu. If a randomly selected student tests positive for the flu, what is the probability they actually have the flu?

STA 100 Exam 1: Take Home Part Due One Week After First Exam Prof. Thistleton

This part of the first exam is worth 20 points out of 100. You may consult your textbook and your classroom notes, but must work independently and may not discuss (verbal, electronic, etc.) the exam with anyone. You also must show all of your work to receive credit.

The data for this assignment are as follow:

-44 -167 12 28 -115 119 118 -4 32 17 -19 72 -59 218 -14 11 106 5 -10 - 29 -134 71 162 -70 85 125 -160 -145 57 -40 68 81 71 129 66 119 -121 -2 -

Construct a histogram with 7 classes using the method discussed in class and in our text. First, fill in the following table:

class number lower and upper limits frequency midpoint lower and upper boundaries 1 2 3 4 5 6 7

Now produce a histogram in SPSS consistent with your table. Be sure to print out a copy of your histogram with your name inserted into the graph (recall: Chart, Add Chart Element, Textbox).