Statistics

Assignment2: Quantitative Methods STAT270
Q1
Letter grades on a Statistics 101 test from a class consisting of 200 students are presented in the pie chart below:

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a. How many students received a “D”?
students
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b. If a “C” or better is required to take Statistics 102, how many students in this class will be eligible to take that course?
students
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c. If 75% of those that received a “B” are international students, how many domestic students also got a “B”?
students
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d. If the top 120 students are exempted from a bonus quiz, what is the minimum grade of those exempted?
Minimum grade:

Q2

A group of 40 students in a library was sampled and the type of laptop they were using was examined. It was found that 12 were using HP, 10 were using Lenovo, 7 were using Dell, 5 were using Microsoft, and 6 were using Apple.
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a. Use the given information to complete the following table:
Laptop Type HP Lenovo Dell Microsoft Apple
Frequency

Relative Frequency

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b. How many degrees will the segment representing “Lenovo” have on a pie chart?
°
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c. What proportion of the students use HP?
%
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d. What is the relative frequency for Apple?
%

Q3
The owner of Blackstone Inc. opened 3 stores in different parts of the city and would like to compare the number of sales transactions made after 2 months of operation. The number of sales transactions at the 3 stores are displayed in the chart below:

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a. What type of chart is being used to compare the data?

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b. Fill in the following two-way frequency table for the data.
Store 1 Store 2 Store 3 Total
Month 1

Month 2

Total

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c. How many transactions were made in the first month?

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d. How many transactions were made in total (in both months at all 3 stores)?

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e. What percent of the total transactions were made by Store 3?
%
Round to one decimal place
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f. What percent of the total transactions were made by Store 3 in Month 2?
%
Round to one decimal place
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g. What percent of the transactions at Store 2 were made in Month 1?
%
Round to one decimal place
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h. What percent of the transactions in Month 1 were made at Store 2?
%
Round to one decimal place
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i. Which store has the highest percentage increase from Month 1 to Month 2?

Q4

The ungrouped frequency table below shows the number of students absent in a statistics class in a fall semester.
Number Absent Number of Classes
0 3
1 3
2 5
3 7
4 6
5 4
6 3
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a. Is it possible to recover the raw data from this table?

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b. What is the total number of absenteeism recorded in the course that semester?

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c. What number of absent students occurred most often?

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d. In how many classes were 2 students absent?

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e. How many times were no more than 2 students absent?

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f. How many times were more than 4 students absent?

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g. What proportion of classes were exactly 4 students absent?

%
Round to two decimal places
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h. What proportion of classes were up to 3 students absent?

%
Round to two decimal places
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i. What proportion of classes were more than 3 students absent?

%
Round to two decimal places
Q5
The year-end dividend yields (%) for a sample of 48 top-performing stocks are shown in the table below:
4.6 5.1 4.7 4.4 4.1 3.7 3.0 2.8 3.6 3.3 3.2 5.6
3.0 5.8 4.8 3.7 5.2 2.6 4.5 5.8 5.1 5.0 3.4 3.3
3.2 3.9 3.5 4.4 3.7 2.6 3.7 2.7 3.2 3.1 2.9 4.0
5.1 3.0 3.5 3.8 4.8 3.7 3.2 4.4 2.9 2.5 3.8 5.3
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a. Fill in the following frequency table using the data.
Dividend Yield Frequency
2.5 to < 3.0 3.0 to < 3.5 3.5 to < 4.0 4.0 to < 4.5 4.5 to < 5.0 5.0 to < 5.5 5.5 to < 6.0 Total 48 ________________________________________ b. What is the frequency of the 3.0 to < 3.5 interval? ________________________________________ c. What proportion of the dividend yields are at least 4.0% but less than 5.0%? % Round to two decimal places ________________________________________ d. What proportion of the dividend yields are less than 4.0%? % Round to two decimal places ________________________________________ e. Suppose a stock is rated A if its dividend yield is 4.0% or higher and rated B if the yield is less than 4.0%. What proportion of B-rated stocks in this sample have dividend yields less than 3.0%? % Round to two decimal places Q6 The amount of time (minutes) a sample of students spent on online social media in a 4-hour window is organized in a frequency distribution with 7 class intervals. The class intervals are 0 to < 10, 10 to < 20, ..., 60 to < 70. The number of observations (frequencies) for the classes are 7, 9, 19, 13, 16, 9, and 7 respectively. ________________________________________ a. Complete the following frequency table for the distribution showing frequency, relative frequency, cumulative frequency, and cumulative relative frequencies. Round to four decimal places when necessary Class Interval Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency 0 to < 10 10 to < 20 20 to < 30 30 to < 40 40 to < 50 50 to < 60 60 to < 70 ________________________________________ b. How many students spent between 40 and 60 minutes on social media? ________________________________________ c. What percent of the students spent between 50 and 60 minutes on social media? % Round to two decimal places ________________________________________ d. What percent of the students spent no more than 40 minutes on social media? % Round to two decimal places ________________________________________ e. What percent of the students spent no less than 50 minutes on social media? % Round to two decimal places Q7 The histogram below summarizes the grades (out of 50) of all students who wrote a midterm exam. ________________________________________ a. How many class intervals were used in the histogram? ________________________________________ b. How many students wrote midterm exam? ________________________________________ c. What is the modal class? ________________________________________ d. What is the midpoint of the last class interval? ________________________________________ e. How many students scored between above 20 but no more than 25? ________________________________________ f. What percent of students scored above 35? % Q8 A3 The following data consists of birth weights (pounds) of a sample of newborn babies at a local hospital: 9.29.37.18.19.49.39.67.78.27.68.29.29.37.18.19.49.39.67.78.27.68.2 Calculate the following: ________________________________________ a. Range Range=Range= ________________________________________ b. Variance s2=s2= Round to 2 decimal places ________________________________________ c. Standard Deviation s=s= Round to 2 decimal places Q10 Given Samples A and B below, Sample A: 4.2 3.5 3.9 3.7 3.5 3.0 2.3 4.9 2.8 Sample B: 4.8 4.8 4.8 2.3 2.9 3.0 4.8 2.5 2.2 ________________________________________ a. Calculate the mean and standard deviation for each sample. Sample A: x̄ A = x̄ A = ; s A = ; s A = Sample B: x̄ B = x̄ B = ; s B = ; s B = Round to two decimal places if necessary Q11 The recommended minimum credit card payment for a sample of 100 credit card holders is summarized below: Minimum Payment ($) Frequency 15 to under 30 36 30 to under 45 31 45 to under 60 19 60 to under 75 5 75 to under 90 9 ________________________________________ a. Estimate the mean minimum payment. Mean: Round to 2 decimal places. ________________________________________ b. Using that median class, estimate the median minimum payment. Median: ________________________________________ c. What is the modal class? Modal Class: ________________________________________ d. Describe the shape of the distribution in terms of symmetry/skewness. Skewness: Q12 A search on Best Barryo Mobile's website for "smartwatch" produced ninety-two results, 40 of which are actual smartwatches. Their prices are summarized in the frequency table below: Price ($) Number of Watches 50 to under 100 3 100 to under 150 5 150 to under 200 7 200 to under 250 6 250 to under 300 13 300 to under 350 6 ________________________________________ a. Calculate an approximate value for the sample variance. s2=s2= Round to two decimal places if necessary ________________________________________ b. Calculate an approximate value for the sample standard deviation. s=s= Round to two decimal places if necessary Q13 A population of score data is normally distributed with a mean of 7.50 and a standard deviation of 0.85. Approximately what percent of the scores will fall between ________________________________________ a. 4.95 and 10.05? % ________________________________________ b. 6.65 and 8.35? % ________________________________________ c. 5.8 and 9.2? % Q14 Outgoing calls at a call centre are completed in 130 seconds on average with a standard deviation of 8 seconds. Suppose call completion times are approximately normal. The shortest 2.5% of the completed calls will last less than how many seconds? seconds