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Statistics 370

 

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Q1

Determine the correct data type for each of the following:

Baseball jersey number (click to select) Qualitative Quantitative (Discrete) Quantitative (Continuous)
Language spoken (click to select) Qualitative Quantitative (Discrete) Quantitative (Continuous)
Distance travelled (click to select) Qualitative Quantitative (Discrete) Quantitative (Continuous)
Number of international calls made (click to select) Qualitative Quantitative (Discrete) Quantitative (Continuous)

 

Q2

The following questions were asked of a group of applicants for a scholarship award. Determine the level of data measurement (nominal, ordinal, interval, ratio) for the bold words in each question.

Question Level of Measurement
What is your date of birth? (click to select) Nominal Ordinal Interval Ratio
What is your total family income? (click to select) Nominal Ordinal Interval Ratio
What is your highest level of education (high school, some college, associate degree, …)? (click to select) Nominal Ordinal Interval Ratio
How much financial aid (dollars) do you think you need? (click to select) Nominal Ordinal Interval Ratio
Would you categorize your need as low, medium, or high? (click to select) Nominal Ordinal Interval Ratio

 

Q3

A local radio station opened a telephone line during a college strike action requesting listeners to respond to the question “Should the government legislate striking professors back to work?” 78% of respondents responded “Yes”.

Identify a potential source of bias in this situation.

Selection Bias

Self-selection Bias

Non-response Bias

Small Sample Bias

Researcher Bias

Unverified Response Bias

Q4

Professors in a Business program are allowed to have a non-contact day during the week excluding Tuesdays. The day of the week preferred by the 40 professors in the program are as follows:

M M Th F W F M W M F
M M M M F F F F M M
F M F M F M F M F W
M F F F M M M W Th W

M = Monday, W = Wednesday, Th = Thursday, F = Friday

  1. Complete the following frequency distribution and relative frequency distribution table for the data.
Preferred Day Frequency Relative Frequency
Monday
Wednesday
Thursday
Friday
Total 40 1
  1. Which day is mostly preferred?

(click to select) Monday Wednesday Thursday Friday

  1. If the data were constructed on a pie chart, what angle will represent Wednesday?

°

Q5

 

Total student enrollment in STAT 102 each semester last year is divided up by semester and summarized the pie chart below. Suppose 1,200 students enrolled in the course last year.

  1. How many students enrolled in the winter semester?
  2. What angle represents the “Summer” segment on the chart?

°

  1. If 20% of students enrolled in the fall were international students, how many of them were domestic?

 

Q6

The table below shows the number of permanent residents admitted to Canada (2015-2017) classified by immigration categories: Economic Class, Family Class and Protected Persons, Refugees, Humanitarian and Compassionate (RHC).

Year Category Total
2015 Economic 171,893
2015 Family 66,663
2015 RHC 36,021
2016 Economic 154,779
2016 Family 82,180
2016 RHC 60,218
2017 Economic 159,018
2017 Family 75,600
2017 RHC 48,395

Use the data to complete the following relative frequency percent table.

Round to two decimal places

Year Economic Family RHC Total
2015 % % % %
2016 % % % %
2017 % % % %
Total % % % 100.00%

 

 

 

 

 

 

 

 

 

 

 

Q7

In order to help new students in selecting better teachers, current students at a college rate their professors’ teaching ability either as Excellent, Good or Poor. Professor Crane’s ratings by 160 students from winter, summer and fall last year are presented in the chart below:

  1. Use the data on the chart to complete the following two-way table.
Excellent Good Poor Total
Winter
Summer
Fall
Total
  1. What proportion of the ratings are from the fall semester?

Round to three decimal places

  1. What proportion of the ratings are poor?

Round to three decimal places

  1. What proportion of the ratings from the winter semester are excellent?

Round to three decimal places

  1. What proportion of all the excellent ratings are from the winter semester?

Round to three decimal places

Q8

Anderson Manufacturing orders four types of components for their new wireless headset from two suppliers. The number of units received from a recent order is summarized in the table below:

Type 1 Type 2 Type 3 Type 4 Total
Supplier 1 130 160 190 150 630
Supplier 2 190 140 140 130 600
Total 320 300 330 280 1,230
  1. What proportion of the units were received from Supplier 2?

Round to three decimal places if necessary

  1. What proportion of the components received were Type 2?

Round to three decimal places if necessary

  1. What proportion of Type 2 units received were from Supplier 1?

Round to three decimal places if necessary

  1. What proportion of the units received from Supplier 2 were Type 3?

Round to three decimal places if necessary

Q9

The amount of time (minutes) spent at a Smart Centre by 40 shoppers are given below.

50 27 18 36 51 54 46 59 56 14
19 54 41 9 45 37 33 48 26 31
52 57 56 47 46 42 55 17 9 43
23 5 57 20 26 27 35 28 44 49
  1. Complete the following frequency distribution for the data.
Class Frequency
0 to < 10
10 to < 20
20 to < 30
30 to < 40
40 to < 50
50 to < 60
Total 40
  1. What is the class midpoint for the second class?
  2. What proportion of the shoppers spent less than 30 minutes at the Smart Centre?
  3. Is the distribution symmetric, skewed left, or skewed right?

(click to select) Symmetric Skewed Left Skewed Right

 

Q10

Percentage point change between midterm and final grades for students in two sections of a stats course are presented in a split back-to-back stem-and-leaf plot as follows:

Section A Section B
-1 1   2
9   8   5 -0 5   6   9
4   3   3   3   1 -0 1   1   1   2
4   4   3   2   2   1   0 0 0   0   0   0   1   2   2   3   3
9   8   7   7   6   5   5   5 0 5   5   6   7   8
4   4   3   3   3   1   1   1   0 1 1   2   4
1 6   8

Key: 2 | -0 | 4 means that the student in section A dropped by 2 percentage points between midterm grade and final grade while the student in section B dropped by 4 points.

(Percentage point change = final grade – midterm grade)

  1. How many students in Section A had a worse final grade than midterm?
  2. How many students in Section B did not experience a grade change?
  3. How many students in Section B improved by more than 10 percentage points?
  4. What proportion of students in Section A improved by more than 10 percentage points?

Round to three decimal places

  1. Calculate the range of percentage point change for Section A.
  2. Calculate the range of percentage point change for Section B.
  3. Describe the shape of the Section A distribution in terms of skewness.

(click to select) Symmetric Skewed Right Skewed Left

  1. Describe the shape of the Section B distribution in terms of skewness.

(click to select) Symmetric Skewed Right Skewed Left

 

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