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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
- 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 |
- Which day is mostly preferred?
(click to select) Monday Wednesday Thursday Friday
- 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.
- How many students enrolled in the winter semester?
- What angle represents the “Summer” segment on the chart?
°
- 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:
- Use the data on the chart to complete the following two-way table.
Excellent | Good | Poor | Total | |
Winter | ||||
Summer | ||||
Fall | ||||
Total |
- What proportion of the ratings are from the fall semester?
Round to three decimal places
- What proportion of the ratings are poor?
Round to three decimal places
- What proportion of the ratings from the winter semester are excellent?
Round to three decimal places
- 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 |
- What proportion of the units were received from Supplier 2?
Round to three decimal places if necessary
- What proportion of the components received were Type 2?
Round to three decimal places if necessary
- What proportion of Type 2 units received were from Supplier 1?
Round to three decimal places if necessary
- 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 |
- 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 |
- What is the class midpoint for the second class?
- What proportion of the shoppers spent less than 30 minutes at the Smart Centre?
- 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)
- How many students in Section A had a worse final grade than midterm?
- How many students in Section B did not experience a grade change?
- How many students in Section B improved by more than 10 percentage points?
- What proportion of students in Section A improved by more than 10 percentage points?
Round to three decimal places
- Calculate the range of percentage point change for Section A.
- Calculate the range of percentage point change for Section B.
- Describe the shape of the Section A distribution in terms of skewness.
(click to select) Symmetric Skewed Right Skewed Left
- Describe the shape of the Section B distribution in terms of skewness.
(click to select) Symmetric Skewed Right Skewed Left
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