Posted: July 25th, 2023
NAME_________________ Score ______ / 50
STAT 200: Introduction to Statistics
Homework #1
Clearly Indicate Your Final Answer
Total Points Earned:
1. ______ / 1
2. ______ / 1
3. ______ / 2
4. ______ / 2
5. ______ / 2
6. ______ / 2
7. ______ / 5
8. ______ / 6
9. ______ / 2
10. ______ / 2
11. ______ / 10
12. ______ / 10
13. ______ / 3
14. ______ / 2
Score ______ / 50
1. (1 point) In a survey of 109 subjects, each was asked to indicate how many text messages they send and receive each day. The sample consisted of those who chose to respond to the request posted on the StatCrunch website. Determine whether this sampling method appears to be sound or is flawed. Explain your answer.
2. (1 point) In a study of the Gender Aide method of gender selection for soon-to-be expecting parents using fertility clinics, 1000 users of this method gave birth to 540 boys and 460 girls. There is about a 1% chance that such extreme results would occur if the method had no effect. Do the results appear to have statistical significance? Do they have any practical significance? Explain your answers.
3. (2 points) Determine whether the described value is a statistic or parameter.
a. (1 point) There are 50 states in the United States.
b. (1 point) In a random sample of households, it was found that 47% of the sampled households had high-definition televisions.
4. (2 points) Which of the four levels of measurement (nominal, ordinal, interval, or ratio) are most appropriate for the statements below?
a. (1 point) The movie Avatar was given 4 out of 5 stars.
b. (1 point) The following car models are used for crash testing: Chevrolet Cruze, Honda Civic, Mitsubishi Lancer, VW Jetta, Dodge Charger, Ford Fusion, Buick Lucerne.
5. (2 points) Identify which type of sampling method is used in the following scenarios (i.e. random, systematic, convenience, stratified, or cluster):
a. (1 point) When collecting data from different sample locations in a lake, a researcher uses the “line transect method” by stretching a rope across the lake and collecting samples at every interval of 5 meters.
b. (1 point) On the day of the latest presidential election, ABC News organized an exit poll in which specific polling stations were randomly selected and all voters were surveyed that left the premises.
6. (2 points) Determine whether the sample described below is a simple random sample. Explain your choice.
a. (1 point) In order to test for a gender gap in the way men and women purchase cars, the Grant Survey Company polls exactly 750 adult men and 750 adult women randomly selected from adults in the United States.
b. (1 point) According to the State of New York Unified Court System, names of potential jurors are selected from a variety of different sources. When a trial requires a jury, names from rhe list are randomly selected in a way that is equivalent to writing the names on slips of paper, mixing them in a bowl, and selecting the required number of potential jurors.
7. (5 points): Answer the following questions about this frequency distribution:
Age (in years) of Actor when Best Actor Oscar was Won |
Frequency |
20 – 29 |
1 |
30 – 39 |
26 |
40 – 49 |
35 |
50 – 59 |
13 |
60 – 69 |
6 |
70 – 79 |
1 |
a. (1 point) What is the Class Width?
b. (1 point) What are the Class Midpoints (total of 6)?
c. (1 point) What are the Class Boundaries (total of 7)?
d. (2 points) Construct a Cumulative Frequency Distribution for this frequency distribution.
8. (6 points) The data set below consists of the times (in minutes) for 48 aircraft to Taxi from the Terminal to the Runway at Atlanta’s Hartsfield International Airport. This data set is also available in the Microsoft Excel file “Homework 1 Data Sets.xlsx”
Time to Taxi Out in Minutes |
|||||||
30 |
37 |
16 |
22 |
15 |
13 |
13 |
22 |
19 |
13 |
14 |
23 |
12 |
15 |
20 |
43 |
12 |
14 |
15 |
16 |
19 |
43 |
12 |
49 |
19 |
15 |
27 |
13 |
18 |
18 |
17 |
45 |
18 |
31 |
19 |
16 |
21 |
17 |
35 |
13 |
22 |
15 |
22 |
18 |
20 |
19 |
19 |
23 |
a. (4 points) Construct a frequency distribution for this data set. Begin with a lower class limit of 10 minutes and use a class width of 5 minutes. Include a column for the Relative Frequency Percentage. Based on your results, does it appear that the time required to taxi can be predicted with reasonable accuracy?
b. (2 points) Construct a histogram from the frequency distribution you created in part a. If the quality of air traffic procedures was improved so that the taxi-out times varied less, would the histogram be affected?
9. (2 points) Construct a stemplot for the data set below on Braking Distance (in feet) required for a car to come to a full stop from 60 miles per hour. Is there any evidence to suggest that the data is not from a population having a normal distribution? This data set is also available in the Microsoft Excel file “Homework 1 Data Sets.xlsx”
CAR |
BRAKING DISTANCE |
Chev Aveo |
133 |
Honda Civic |
136 |
Mitsubishi Lancer |
126 |
VW Jetta |
137 |
Hyundai Elantra |
138 |
Kia Rio |
132 |
Subaru Impreza |
135 |
Ford Fusion |
136 |
Nissan Altima |
136 |
Nissan Maxima |
128 |
Honda Accord |
140 |
Volvo S60 |
140 |
VW Passat |
135 |
Toyota Camry |
137 |
Toyota Avalon |
139 |
Hyundai Azera |
134 |
Cadillac DTS |
145 |
Lincoln Town |
143 |
Dodge Charger |
131 |
Merc Gr Marq |
140 |
Buick Lucerne |
143 |
10. (2 points) Use the data set below on weights and volumes of Coke in a can to construct a scatterplot. Does there appear to be a correlation between volume and weight? What else is notable about the arrangement of points, and how can it be explained? This data set is also available in the Microsoft Excel file “Homework 1 Data Sets.xlsx”
Regular Coke Weight (lbs) |
Regular Coke Volume (ounces) |
0.8192 |
12.3 |
0.815 |
12.1 |
0.8163 |
12.2 |
0.8211 |
12.3 |
0.8181 |
12.2 |
0.8247 |
12.3 |
0.8062 |
12 |
0.8128 |
12.1 |
0.8172 |
12.2 |
0.811 |
12.1 |
0.8251 |
12.3 |
0.8264 |
12.3 |
0.7901 |
11.8 |
0.8244 |
12.3 |
0.8073 |
12.1 |
0.8079 |
12.1 |
0.8044 |
12 |
0.817 |
12.2 |
0.8161 |
12.2 |
0.8194 |
12.2 |
0.8189 |
12.2 |
0.8194 |
12.2 |
0.8176 |
12.2 |
0.8284 |
12.4 |
0.8165 |
12.2 |
0.8143 |
12.2 |
0.8229 |
12.3 |
0.815 |
12.2 |
0.8152 |
12.2 |
0.8244 |
12.3 |
0.8207 |
12.2 |
0.8152 |
12.2 |
0.8126 |
12.1 |
0.8295 |
12.4 |
0.8161 |
12.2 |
0.8192 |
12.2 |
11. (10 points) Listed below are the annual (yes, that means every YEAR) tuition amounts of the 10 most expensive colleges in the United States for a recent year. The colleges listed in order are Sarah Lawrence, NYU, George Washington, Bates, Skidmore, Johns Hopkins, Georgetown, Connecticut College, Harvey Mudd, and Vassar. This data set is also available in the Microsoft Excel file “Homework 1 Data Sets.xlsx”
$ 54,410 |
$ 51,991 |
$ 51,730 |
$ 51,300 |
$ 51,196 |
$ 51,190 |
$ 51,122 |
$ 51,115 |
$ 51,037 |
$ 50,875 |
a. (2 points) What is the mean cost of college tuition for the 10 most expensive colleges?
b. (1 point) What is the median cost of college tuition for the 10 most expensive colleges?
c. (1 point) What is the mode of the cost of college tuition for the 10 most expensive colleges?
d. (1 point) What is the midrange cost of college tuition for the 10 most expensive colleges?
e. (1 point) What is the range of college tuition for the 10 most expensive colleges?
f. (2 points) What is the standard deviation of college tuition for the 10 most expensive colleges?
g. (1 point) What is the variance of college tuition for the 10 most expensive colleges?
h. (1 point) What does this “Top 10” list tell us about the population of all U.S. college tuitions?
12. (10 points) According to the “Freshman 15” legend, college freshman gain 15 pounds (or 6.8 kilograms) during their freshman year. Listed below are the amounts of weight change (in kilograms) for a simple random sample of freshman included in a recent study. Positive values correspond to students who gained weight and negative values correspond to students who lost weight. This data set is also available in the Microsoft Excel file “Homework 1 Data Sets.xlsx”
a. (2 points) What is the mean weight change (in kilograms) for the data sample?
b. (1 point) What is the median weight change (in kilograms) for the data sample?
c. (1 point) What is the midrange of weight change (in kilograms) for the data sample?
d. (1 point) What is the range of weight change (in kilograms) for the data sample?
e. (2 points) What is the standard deviation of weight change (in kilograms) for the data sample?
f. (1 point) What is the variance of weight change (in kilograms) for the data sample?
g. (1 point) Do the values appear to support the legend that college students gain 15 pounds (or 6.8 kilograms) during their freshman year? Why or why not?
13. (3 points) When Steve Jobs was the Chief Executive Officer (CEO) of Apple, he earned an annual salary of $1. The CEOs of the 50 largest U.S. companies had a mean salary of $1,449,779 and a standard deviation of $527,651 (based on data from USA Today). This data set is also available in the Microsoft Excel file “Homework 1 Data Sets.xlsx”
a. (1 point) How many standard deviations are there between Steve Jobs’ salary and the mean CEO salary?
b. (1 point) Convert Steve Jobs’ salary to a z-score.
c. (1 point) If we consider “usual” salaries to be those that convert to z-scores between -2 and 2, is Steve Jobs’ salary usual or unusual?
14. (2 points) The data below are the interval times (in minutes) between eruptions of the Old Faithful geyser in Yellowstone National Park (based on data from the U.S. National Park Service). This data set is also available in the Microsoft Excel file “Homework 1 Data Sets.xlsx”
81 |
81 |
86 |
87 |
89 |
92 |
93 |
94 |
95 |
96 |
97 |
98 |
98 |
101 |
101 |
106 |
Use this data to determine the 5-number summary and construct a box-plot.
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