MATH 2228 Exam 1 (Questions 1-7)

Question 6: Consider two graphs for the amount of the first bill for 80 new residential phone customers. At least one graph will contain sufficient information to answer any question. Exactly, find the 8th percentile of the 80 bill amounts. Note: the lowest 21 amounts are visible, the middle 56 are obscured by the coffee spill, and the highest 3 amounts are also visible.

$39

Question 4: Consider the frequency bar chart below which summarizes data collected on 500 randomly selected ECU students. Diet Pepsi and Diet Mt Dew are both products of PepsiCo. What percentage of the sample last had a PepsiCo product?

43%

Question 5: The 5 largest data values were: 42 44 50 70 80 The two largest values were found to be outliers. The upper whisker on the boxplot hasnt been drawn. It would extend from the top of the box (30) up to _____?

50

Question 3: Each person in a sample of five people was asked to report the amount of change (in cents) in his/her pockets. Their answers were 0, 11, 16, 25, 33 Calculate the sample mean. The appropriate symbol is _________ = __________

bar, 17

Question 6: Consider two graphs for the amount of the first bill for 80 new residential phone customers. At least one graph will contain sufficient information to answer any question. Answer yes or no as to whether or not each of the following describes the shape of the distribution:

Unimodal? yes, unimodal Uniform / Evenly Distributed? no, not uniform

Question 3: There is a negative correlation between the number of flu cases reported each week throughout the year (call this variable X) and the amount of ice cream (call this variable Y) sold that week. The most plausible explanation for this association is:

changes in X and Y are due to a common response to other variables: winter months see low ice cream sales and simultaneously high numbers of flu cases. Vice versa for summer months.

Question 1: If the company had randomly selected 500 addresses from all residual addresses, which type of sampling would they have employed?

simple random sample

Question 5: The 5 largest data values were: 42 44 50 70 80 The two largest values were found to be outliers. Suppose that the average ticket is purchased 29 days in advance. Comparing this mean to the median, we can deduce that the data is __________ since, ______________.

skewed right; mean is greater than the median

Question 6: Consider two graphs for the amount of the first bill for 80 new residential phone customers. At least one graph will contain sufficient information to answer any question. What is the relative frequency of bill amounts that are at least 90?

12.5%

Question 5: The 5 largest data values were: 42 44 50 70 80 The two largest values were found to be outliers. Reading the boxplot, what is the value of the IQR?

16

Question 7: A production manager has compared the dexterity-test scores of nine assembly line workers with their hourly productivity in the following scatterplot: The table below summarizes the data: Productivity: Sample Mean = 62.56 Sample Standard Deviation = 7.28 Dexterity: Sample Mean = 14.56 Sample Standard Deviation = 2.35 Predict the productivity of a worker with a dexterity of 15.

63.8

Question 4: Consider the frequency bar chart below which summarizes data collected on 500 randomly selected ECU students. Which diet soda represents the mode of the data? Hint: the original data is a list of 500 diet sodas.

Diet Pepsi

Question 1: The utility company in the city of Harperville serves 20,000 residential addresses. The company wants to gauge interest in a "Beat the Peak" program which offers consumers a discount in exchange for limited electricity usage during peak hours. Unknown to the utility company, 18% of its 20,000 residential customers would participate in such a program. Since the company does not know the level of interest among its customers, the company selects every 40thaccount from an alphabetical listing of residential account holders, starting with the 23rd name. Of the 500 subscribers selected, 16% express interest in the "Beat the Peak" program. The company also gathered other information from the 500 sampled accounts: First, indicate whether each of the above variables is categorical or quantitative. Next, indicate whether each categorical variable is nominal or ordinal and indicate whether each quantitative variable is discrete or continuous.

Number of people living in the household: Quantitative, Discrete Most frequently watched cable channel: Categorical, Nominal Method of payment for utility bill (e.g. check): Categorical, Nominal Electrical usage last month: Quantitative, Continuous

Question 7: A production manager has compared the dexterity-test scores of nine assembly line workers with their hourly productivity in the following scatterplot: The table below summarizes the data: Productivity: Sample Mean = 62.56 Sample Standard Deviation = 7.28 Dexterity: Sample Mean = 14.56 Sample Standard Deviation = 2.35 Find the least squares regression line which uses Dexterity to predict Productivity.

The slope is b = 2.82 The y-intercept is a = 21.5

Question 1: If the company had randomly selected 50 neighborhoods within its service area and solicited opinions from every customer in those neighborhoods, which type of sampling would they have employed?

cluster

Question 4: Consider the frequency bar chart below which summarizes data collected on 500 randomly selected ECU students. Would this data be considered cross-sectional or time-series?

cross sectional

Question 1: The utility company notes that, in the sample, there were at least 4 customers not interested for every 1 customer that was interested. This statement reflects_________

descriptive statistics

Question 4: Consider the frequency bar chart below which summarizes data collected on 500 randomly selected ECU students. Which one of the following explanations addresses why it would be inappropriate to conclude that the distribution of diet sodas last drank is skewed to the right?

ii) The data is nominal. The categories thus could be arranged to appear symmetric or even skewed left.

Question 7: A production manager has compared the dexterity-test scores of nine assembly line workers with their hourly productivity in the following scatterplot: The table below summarizes the data: Productivity: Sample Mean = 62.56 Sample Standard Deviation = 7.28 Dexterity: Sample Mean = 14.56 Sample Standard Deviation = 2.35 Interpreting the regression line, for every extra unit of dexterity a worker has, the productivity tends to __________ by about _________.

increase; 2.82

Question 2: Consider the 3 summaries presented. Which one is nonsensical? In other words, which one doesn't have any meaning?

mean zipcode

Question 6: Consider two graphs for the amount of the first bill for 80 new residential phone customers. At least one graph will contain sufficient information to answer any question. Half the bill amounts were less than $58 and half the bill amounts were more than $58. The value $58 is thus which measure of center?

median

Question 1: The utility company in the city of Harperville serves 20,000 residential addresses. The company wants to gauge interest in a "Beat the Peak" program which offers consumers a discount in exchange for limited electricity usage during peak hours. Unknown to the utility company, 18% of its 20,000 residential customers would participate in such a program. Since the company does not know the level of interest among its customers, the company selects every 40thaccount from an alphabetical listing of residential account holders, starting with the 23rd name. Of the 500 subscribers selected, 16% express interest in the "Beat the Peak" program. Match the term on the left to its corresponding example from this scenario.

population = all residential utility customers population size, N = 20,000 sample size, n = 500 variable of interest or concern = interest in joining the "beat the peak" program a parameter (not population size) = 18% a statistic (not sample size) = 16%

Question 1: What type of sampling did the utility company employ?

systematic

Question 2: In a sample: - the youngest person sampled was 18 years old - the oldest person sampled was 78 years old Therefore, 60 years is what measure of spread?

range

Question 3: Each person in a sample of five people was asked to report the amount of change (in cents) in his/her pockets. Their answers were 0, 11, 16, 25, 33 Calculate the sample standard deviation of the amounts. The appropriate symbol is _________ = __________

s, 12.71

Question 1: Based on the sample, the utility company concludes that over 10% of its 20,000 residential accounts are interested in the "Beat the Peak" program. This statement reflects _________

statistical inference

Question 1: The utility company divides its service area into 5 zones. If the company had randomly selected 100 customers from each zone, which type of sampling would they have employed?

stratified

Question 2: A population consists of numbers with mean 205 and standard deviation 25. Match the following: z-score associated within a value of 210 value whose z-score is -1.6 If the population values are approximately bell-shaped, then the value __________ represents the approximate 16th percentile of the numbers knowing nothing of the shape of the population, I can conclude that at least __________% of the numbers are between 155 and 255. If the population values are approximately bell-shaped, I can conclude that approximately __________% of the numbers are between 155 and 255.

z-score associated within a value of 210 0.2 value whose z-score is -1.6 165 If the population values are approximately bell-shaped, then the value __________ represents the approximate 16th percentile of the numbers 180 knowing nothing of the shape of the population, I can conclude that at least __________% of the numbers are between 155 and 255. 75% If the population values are approximately bell-shaped, I can conclude that approximately __________% of the numbers are between 155 and 255. 95%