MA116A Elements of Statistics – Exam 1 by Daeshik Park
Student’s Name: Student’s Score: /100
Directions:You must show your work in every detail and use complete sentences to describe your answers; otherwise you will get heavy penalty.Write neatly your work for each problem by circlingyour answers if possible.Round all numbers to two decimal places if needed. No calculator features if not indicated.
1. [6 points] Classify and circle the aspect of statistics for each statement.
a) From past figures, it is predicted that 47% of the registered voters in Virginia will vote in the June primary.Circle your answer: Design, Description or Inference.
b) The average age of the students in a statistics class is 25 years.
Circle your answer: Design, Description or Inference.
2. [3 points] To estimate the percentage of defective items a machine is producing, a quality control analyst inspects the first 100 items produced in a day. Does this technique produce a random sample?
3. [6 points] Determine whether the summary measure is better described as a parameter or a statistic.
a) The average GPA of a university's graduating class.Circle your answer: Parameter or Statistic.
b) The proportion of teenagers in a nationwide survey who stated that they consumed alcohol on a regular basis.Circle your answer: Parameter or Statistic.
Page 1 of 4
4. [6 points] The following table shows the heights of the five tallest mountains in North America.
Page 1 of 4
McKinley20,3201
Logan19,8502
Citlaltepec18,7003
St. Elias18,0084
Popocatepetl17,9305
a) Is the variable Height discrete or continuous?
b) Is the variable Rank discrete or continuous?
Page 1 of 4
5. The following data provide the daily protein intake (in grams of protein per kilogram of body weight) for 14 competitive athletes.
3.5 / 2.2 / 2.7 / 1.7 / 2.3 / 1.5 / 2.81.8 / 2.0 / 2.0 / 1.9 / 1.7 / 1.8 / 1.6
a) [8 points] Find the mean and the median.
b) [5 points] Which measure of center seems more appropriate for this dataset? Explain.
Page 1 of 4
6. [6 points] Below is the enrollment for fall semester at University X.Construct a bar graph for these data.
7. [6 points] A competency test has scores with a mean of 69 and a standard deviation of 4. A histogram of the data shows that the distribution is normal. Use the Empirical Rule to find the percentage of scores between 61 and 77.Justify your answer.
8. A sample of fifty motorists was taken on a Federal highway where the speed limit was 60 miles per hour. A dot plot of their speeds is shown below.
a)[6 points] What proportion of the motorists was speeding?
b) [3 points] What is the mode for speed?
Page 1 of 4
9. The following frequency histogram provides average SO2 (sulfur dioxide) emission rates from utility and industrial boilers (lb/million Btu) for 47 states (data for Idaho, Alaska, and Hawaii omitted).
a)[3 points] Describe the shape of the distribution.
b) [3 points] What information can you get from the dot plot or stem-and-leaf plot of these data that you cannot get from this plot?
c) [3 points] This histogram shows frequencies. If you were to construct a histogram using the percentagesfor each interval, how (if at all) would the shape of this histogram change?
Page 1 of 4
10. A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below.
Page 1 of 4
a) [3 points] What is the mode rating?
b) [6 points] What percentage of the respondents rated overall television quality as good (regarded as ratings of 70 and above)?
Page 1 of 4
11. [7 points] The weight for adult males in the U.S. follows a bell-shaped distribution with a mean weight of 173 pounds and a standard deviation of 30 pounds. Using the z-score approach for detecting outliers, which of the weights, 110 pounds, 157 pounds, 281 pounds, would represent potential outliers in the distribution of U.S. adult male weights? Explain why.
12. A recent survey investigated exposure to tobacco and alcohol use in a series of G-rated animated films.Data on the total tobacco exposure time (in seconds) is below.
223 / 176 / 548 / 37 / 158 / 51 / 299 / 37 / 11165 / 74 / 9 / 2 / 6 / 23 / 206 / 9
a) [6 points] Find the Five-Number Summary of the datausing calculator features.
b) [7 points] Use the 1.5xIQR Criterion to find any potential outliers of the data.
c) [7 points] Construct a box plot for these data.
Page 1 of 4