MTH 133

EXAM 1

1) What is statistics?– Statistics is the science of collecting, organizing, summarizing and analyzing information in order to draw conclusions.

2) What is the difference between a population and a sample? Provide examples. – A population is the group to be studied in a statistical analysis and a sample is a smaller subset of that population, e.g. a population could be all of the residents of Lenawee county and a sample would be 1000 randomly selected people from that group.

3) A study was conducted to determine if listening to heavy metal music affects critical thinking. To test the claim, 114 subjects were randomly assigned to two groups. Both groups were administered a basic math skills exam. The first group took the exam while heavy metal music was piped into the exam room, while the second group took the exam in a silent room. The mean exam score for the first group was 80, and the mean exam score for the second group was 87. The researchers concluded that heavy metal music negatively affects critical thinking. Identify:

a) the research objective – to find out if heavy metal music affects critical thinking

b) the sample - 114 randomly selected subjects

c) the descriptive statistics – The mean exam score for the group who took the test while listening to heavy metal music was 80, the mean exam score for the group who took the test without heavy metal music was 87.

d) the conclusions – Heavy metal music negatively affects critical thinking.

3) Classify the numbers on the shirts of a girl's soccer team as qualitative data or quantitative data.

A) qualitative dataB) quantitative data

4) Classify the number of seats in a movie theater as qualitative data or quantitative data.

A) qualitative dataB) quantitative data

5) The number of violent crimes committed in a day possesses a distribution with a mean of 1.1 crimes per day and a standard deviation of four crimes per day. A random sample of 70 days was observed, and the sample mean number of crimes for the sample was calculated. The data that was collected in this experiment could be measured with a ______random variable.

A) continuousB)discrete

6) Classify the following random variable according to whether it is discrete or continuous.age of the oldest student in a statistics class

A) discreteB)continuous

7) N/A

8) The following frequency distribution represents the total ticket sales for 5 major rock acts for concerts on March 3, 2005 in various New York City venues:

Band / # of tickets sold
Metallica / 10,735
Slipknot / 9,422
Mastodon / 1,064
Slayer / 3,456
Machine Head / 732

a) Construct a relative frequency distribution

Band / # of tickets sold / Relative Frequency
Metallica / 10,735 / .422
Slipknot / 9,422 / .371
Mastodon / 1,064 / .042
Slayer / 3,456 / .136
Machine Head / 732 / .029

b) What percentage of tickets were sold by Metallica? 42.2%

c) Construct a frequency bar graph

d) Construct a relative frequency bar graph.

e) Construct a pie chart

9) Using the data for per capita income for Michigan counties, do the following:

a) Construct a frequency distribution of the data.

b) Construct a relative frequency distribution of the data (can be put in the same table as part a)

c) Construct a frequency histogram of the data. Describe the shape of the distribution

The distribution is skewed right.

10) The following data represent the number of hours a group of 40 community college students studied each day:

1.2 / .3 / 4.5 / 2.3 / 3.2 / 3.2 / 1.7 / 1.9
3.4 / .1 / .9 / 6.5 / 3.4 / 2.4 / 1.3 / 1.6
2.8 / .7 / .1 / 3.4 / 3.5 / 2.7 / 2.9 / 2.2
3.1 / 1.5 / 1.7 / 1.9 / 3.9 / 3.3 / 2.9 / 2.8
1.6 / .7 / 2.8 / 2.0 / 3.0 / 3.1 / 2.6 / 2.7

a)Compute the mean – 2.395

b)Compute the range – 6.4

c)Compute the variance – 1.54

d)Compute the standard deviation – 1.24

e)Pick a random sample of 10 students and repeat a through d

1.2 / 4.5 / 1.7 / .9 / 2.4 / 1.6 / 3.5 / 2.2
1.5 / 2.8

f)Compute the mean – 2.23

g)Compute the range – 3.6

h)Compute the variance – 1.24

i)Compute the standard deviation – 1.11

11) A random sample of 30 new cars was taken to find out how many days a new vehicle can go before it must be professionally repaired (excluding routine oil changes). The study found a mean of 325 days, with a standard deviation of 30 days. Assume that a histogram of the data turns out to be bell shaped.

a) 99.7% of the cars will go between235 and 415 days before having to be repaired.

b) Determine the percentage of cars that will go between 265 and 385 days without needing repair.95%

c) If the auto company guarantees free repair for cars up until 265 days, what percentage of cars will they have to repair for free?2.5%

12) Joe receives the following list of grades at the end of his winter term:

Biology / 78
English / 87
Mathematics / 65
French for Beginners / 70
Adventures in Art / 95

:

a)Based on this information, what is his grade average for the term?79%

b)What would Joe have to make in Math to give himself a grade average of 85?95%

c)Assuming that Biology, English and Math are all worth 3 credits, and French and Art are 2, what is his grade average? 78.46%

d)Given this situation, what would Joe have to make in Math to yield a grade average of 85?93.33%

13) The following data represent the number of live multiple delivery births (three or more babies for women 15-49 years old:

Age / Number of Multiple Births
15-19 / 78
20-24 / 385
25-29 / 1587
30-34 / 2854
35-39 / 1986
40-44 / 243
45-49 / 56

a)Approximate the arithmetic mean and the standard deviation age.Mean = 32.03, Standard deviation = 5.04

14) The following data represent the results of a study of 1000 random men and women between the ages of 15 and 49 to find out how many days a year they spend thinking about statistics.

Age / Days thinking about Statistics
15-19 / 2
20-24 / 24
25-29 / 56
30-34 / 125
35-39 / 245
40-44 / 98
45-49 / 21

a) Approximate the arithmetic mean and the standard deviation age.Sample Mean = 35.45, Standard deviation = 5.63