Midterm Exam

 

1.  On a test, 23% of the questions are answered correctly. If 88 questions are correct, how many questions are on the test?

 

2.  After inspecting all of 4400 kg of meat stored at the Wurst Sausage Company, it was found that 957 kg of the meat was spoiled. Determine whether the given value is a statistic or a parameter.

1. The value is a statistic because it is a numerical measurement describing some characteristic of a sample.  
2. The value is a parameter because it is a numerical measurement describing some characteristic of a sample.  
3. The value is a statistic because it is a numerical measurement describing some characteristic of a population. 
4. The value is a parameter because it is a numerical measurement describing some characteristic of a population. 

 

3   Weight of gravel in a pile is 120 lb. Is the value from a discrete or continuous data set?

1. The data set is neither continuous nor discrete. 
2. A discrete data set because the possible values can be counted.  
3. A continuous data set because there are infinitely many possible values and those values can be measured.  
4. A continuous data set because there are infinitely many possible values and those values can be counted. 

 

4.   Ages of children. Which level of measurement is most appropriate for this data?

1. ratio 
2. interval 
3. nominal  
4. ordinal 

 

5.  A sample consists of every 49th student from a group of 496 students. Identify the type of sampling used.

1. cluster 
2. stratified 
3. convenience 
4. random 
5. systematic 

 

6.  An ad for seat belts claimed that proper usage of seat belts “reduces the chance of fatality in a car crash by 400 percent.” What is wrong with this statement? Choose the correct answer below.

1. The actual amount of the decrease in fatalities is less than 100%. 
2. If fatalities fell by 100%, it would be cut in half. Thus, a decrease of 200% means that it would be totally eliminated, and a decrease of more than 200% is impossible. 
3. The statement does not mention the initial amount of fatalities.
4. If seat belts eliminated all fatalities, it would result in a 100% reduction, so it is not possible to reduce fatalities by more than 100 %. 

 

7.   Explain why using self-reported data instead of measured data is a potential pitfall in data collection. Be sure to include an example.

 

8.   Quiz scores of statistics students were obtained by a teacher and listed below. Construct a frequency distribution beginning with a lower class limit of 0 and use a class width of 2. What frequency is listed for the second class?
0, 5, 5, 4, 2, 6, 9, 2, 5, 10

 

9.  In a survey, 26 voters were asked their ages. The results are shown below. Construct a frequency polygon to represent the data (with 5 classes beginning with a the first data midpoint of 24.5 and a class width of 10). What is the lower class limit of the third class?

58, 57, 43, 40, 24, 50, 68, 63, 41, 58, 58, 27, 36, 36, 22, 56, 33, 43, 60, 31, 24, 41, 39, 44, 60, 55

 

10.   A parcel delivery service lowered its prices and finds that it has delivered twice as many parcels this year as it did last year. To illustrate this fact, the manager draws a cube for last year and a cube for this year with a side length twice the length of last year’s cube.  Draw the manager’s graph. Why is this graph misleading? What visual impression is created by the graph?

 

11.   Listed below are the amounts of time (in months) that the employees of a restaurant have been working at the restaurant. Find the mean. Round your answer to one more decimal place than is present in the original data values.

98, 14, 146, 117, 104, 136, 7, 116, 145, 106, 94, 109

 

12.  Listed below are the amounts of time (in months) that the employees of a restaurant have been working at the restaurant. Find the median. Round your answer to one more decimal place than is present in the original data values.

10, 47, 127, 138, 1, 27, 10, 131, 110, 2, 3, 22

 

 

13  

Find the mode(s) for the given sample data. (If there are more than one, enter the largest value for credit. If there is no mode, enter 0 for credit.)

1, 1, 1, 1, 2, 2, 2, 15

 

14.   Listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. Positive values correspond to women who gained weight and negative values correspond to women who lost weight. What is the standard deviation of the weight change? Round your answer to one more decimal place than is present in the original data values.

-5, -14, 19, 18, -8, -12, -16,-9, -12, 1, 4, 3

 

15.   The highway speeds of cars are summarized in the frequency distribution below. Find the standard deviation of the frequency distribution. Round your answer to one more decimal place than is present in the original data values.

Speed (mph) / Cars 
   30-39    / 8   
   40-49    / 19
   50-59    / 13
   60-69    / 6
   70-79    / 12

 

16.  The mean height of a basketball team is 6.3 feet with a standard deviation of 3 feet. The team’s center is 5.7 feet tall. Find the center’s z score.

 

17.   A weight of 294 pounds among a population having a mean weight of 192 pounds and a standard deviation of 19 pounds. Determine if the value is unusual. Explain. Enter the number that is being interpreted to arrive at your conclusion rounded to the nearest hundredth.

 

18.  Use the given sample data to find Q3. 

43, 51, 69, 50, 42, 61, 43, 57

 

19   Find the percentile for the data value.

Data set: 77, 57, 63, 39, 85, 76, 94, 54, 12, 65, 76, 43, 68, 99, 51, 42;

data value: 94

 

 

20.  Which is better, a score of 72 on a test with a mean of 70 and a standard deviation of 9, or a score of 266 on a test with a mean of 242 and a standard deviation of 25? Enter the better test score.

 

21.    The test scores of 16 students are listed below. Construct a boxplot for the data set. Enter the maximum value.

12, 81, 18, 23, 50, 75, 103, 90, 68, 41, 21, 8, 88, 65, 30, 27