Statistics Exam #1

Kevin asked some of his friends how many hours they had worked during the previous week at their after-school jobs. The results are shown below. Construct a frequency distribution. Use 4 classes. Find relative frequencies. 6 5 6 3 6 6 9 8 6 3 8 5 5 8 6 5 8 6 5 8 5 8 8 3 Hours: Frequency: Relative Frequency: Sum= Sum=

(Class Width= (max-min)/# classes = (9-3)/4 = 1.5 = 2 (Hours is +2) Hours: Frequency: Relative Frequency: 3-4 3 3/24= 0.13 5-6 13 13/24= 0.54 7-8 7 7/24= 0.29 9-10 1 1/24= 0.04 11-12 Sum= 24 Sum= 1

Use the Empirical Rule to answer the question. IQ scores have a mean of 100 and a standard deviation of 15. What percentage of people have the IQ score between 70 and 130? A) 68% B) 95% C) 99.7% D) 100%

(Draw image) (Standard deviation) Answer: B) 95%

Use the given sample data to find the 5-Number Summary. 49 52 52 52 74 67 55 55

(Use TI-84 calculator) Answer: Min: 49 Q1: 52 Med (Q2): 53.5 Q3: 61 Max: 74

The ages (in years) of the eight passengers on a bus are listed below. Find the median age. 10 7 26 16 21 43 40 30 A) 21 B) 23.5 C) 26 D) 24.5

(Use TI-84 calculator) L1 ---> Answer: B) 23.5

Use the given data to find the equation of the regression line y = ax + b (X): 6 8 20 28 36 (Y): 2 4 13 20 30 A) y = 0.897x - 2.79 B) y = 0.801x - 3.79 C) y = 0.95x - 2.79 D) y = 0.897x - 3.79

(Use TI-84 calculator) L1 ---> (X): 6 8 20 28 36 L2 ---> (Y): 2 4 13 20 30 Answer: D) y = 0.897x - 3.79

Define Linear Correlation: Positive Correlation- Negative Correlation-

-A positive correlation exists when both variables increase (or decrease) at the same time. Example: A child's height and weight - the taller the child, generally, the more the child weighs. A positive linear correlation has a positive correlation coefficient and a data cloud that goes from the lower left to the upper right. -In a negative correlation, as one variable increases, the other variable decreases (and vice versa). Example: Amount of money I spent in a month versus the amount of money I put in savings. A negative linear correlation has a negative correlation coefficient and a data cloud that goes from the upper left to the lower right

Define: Cluster: Stratified Sample:

-Cluster sample: Divide the population area into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters -Stratified sample: The population is divided into groups that have a characteristic in common (stratum, plural - strata). For example: age, gender, college major, or income etc. Then a random sample from each group is taken.

Define: -Convenience sample: -Multistage Sampling: -Voluntary response sample:

-Convenience sample: Use results that are easy to get. Usually, the results will be affected by bias. Try to AVOID convenience samples in scientific work. -Multistage Sampling: Collect data by using some combination of the basic sampling methods -Voluntary response sample: The respondents select themselves. Do NOT use voluntary response samples in scientific work.

Define: Random sample: Systematic sample:

-Random sample: (the best sample!) Each individual member has an equal chance of being selected. A random sample avoids bias, but usually is expensive. -Systematic sample: Surveying /Drawing every nth person / item on the list or production line. (The first number should be selected at random.)

Describe the Histogram: Bell Shape- Gaps-

1. (Bell) Shape: Symmetrical - when folded vertically, both sides are (more or less) the same. -Skewed to the right (or left) - has a tail to the right (or left). Sometimes we have neither symmetry nor is the graph skewed. 2. Gaps: Describe where the gaps are (the classes with zero frequencies). Note: The presence of gaps can show that we have data from two or more different populations

The frequency table below shows the number of days off in a given year for 30 police detectives. Days off Frequency Class Midpoint 0-2 10 3-5 1 6-8 7 9-11 7 12-14 1 15-17 4 a) Find midpoint for each class and fill out the third column in the table above. b) Construct a histogram. Use class upper limits or the class midpoints for the horizontal scale. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | c) What is the modal class? ___________________________ d) Are there any gaps or outliers? ____________________________

Days off Frequency Class Midpoint (+3) 0-2 10 (0+2)/2 = 1 3-5 1 (3+5)/2 = 4 6-8 7 7 9-11 7 10 12-14 1 13 15-17 4 16 a) Find midpoint for each class and fill out the third column in the table above. b) Construct a histogram. Use class upper limits or the class midpoints for the horizontal scale. | | | | | | | | | | | | | | | | | | | | | | | SHADE IN THE BAR GRAPH | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | c) What is the modal class? 0-2, Frequency 10 d) Are there any gaps or outliers? no, no

Define: Observational study- Experiment-

Observational study vs. Experiment: In a observational study, measurements are taken from subjects as they are and without any attempt to modify them; while in an experiment, measurements are taken from subjects at least some of which have been modified in order to assess the effects of the modification

Define Level of Measurement: Ordinal- Nominal- Ratio- Interval-

Ordinal- categories with some order (Example: Course grades A, B, C, D, or F) Nominal- categories only (Example: Survey responses yes, no, undecided) Ratio- differences and a natural starting point (Example: Prices of college textbooks) Interval- differences but no natural starting point (Example: Years 1000, 2000, 1776, and 1492)

Define Types of Data: Parameter- Statistic-

Parameter - a numerical measurement describing some characteristic of a Population. Statistic - a numerical measurement describing some characteristic of a Sample

Define: Population- Sample-

Population - is the entire group of individuals or objects that we want information about. (NOT just the ones we reach!) Sample - is the part of the population that is actually observed /surveyed. (The ones we reach.)

(Identify the sample and population. Determine whether the sample is likely to be representative of the population) An ARCC student conducted a survey about the number of smoking college students. She asked every third student standing outside of a classroom building between classes whether or not the person smokes. Her survey compiled the answers of 92 students. Population: ________________________________ Sample: _______________________ Is the sample representative? Why or why not?_______

Population: __College students___ Sample: ____92 students______ Is the sample representative? Why or why not?__Not, the sample is convenience (time and places) Biased._____

Use the range rule of thumb to estimate the standard deviation. The maximum value of a distribution is 23.6 and the minimum value is 7.4. A) 9.1 B) 1.1 C) 18.9 D) 4.1

S= (max-min)/4 = (23.6-7.4)/4 = 4.1 Answer: D) 4.1

Define: Outliers- Modal Class-

3. Outliers - data located far to the right or left from the main body of the histogram. Look for bars following gaps. 4. Modal class (the tallest bar) in the histogram is the class with the highest frequency.

(Determine whether the given value is from a discrete or continuous data set). The number of freshmen entering college in a certain year is 621.

A) Discrete

(Determine which of the four levels of measurement is most appropriate). Survey responses of "good, better, best". A) Ordinal B) Nominal C) Ratio D) Interval

A) Ordinal (logical order)

(Determine whether the given value is a statistic or a parameter). A sample of 120 employees of a company is selected, and the average age is found to be 37 years.

A) Statistic

(Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience) A sample consists of every 49th student from a group of 496 students. A) Systematic B) Stratified C) Random D) Cluster E) Convenience

A) Systematic

Dave is a college student contemplating a possible career option. One factor that will influence his decision is the amount of money he is likely to make. He decides to look up the average salary of graduates in that profession. Which information would be more useful to him, the mean salary or the median salary? Why?

Answer: Median: Data not consistent; Outliers

(The frequency distribution below summarizes employee years of service for Alpha Corporation. Determine the width of each class) Years of Service Frequency 1 - 5 5 6 - 10 20 11 - 15 25 16 - 20 10 21 - 25 5 26 - 30 3 A) 4 B) 5 C) 10 D) 6

B) 5

(Determine whether the given description corresponds to an observational study or an experiment) A marketing firm does a survey to find out how many people use a product. Of the one hundred people contacted, fifteen said they use the product. A) Experiment B) Observational study

B) Observational study (No treatment)

(Determine if the sampling plan results in a simple random sample) A researcher obtains an alphabetical list of the 2560 students at a college. She uses a random number generator to obtain 50 numbers between 1 and 2560. She chooses the 50 students corresponding to those numbers. A) No. The sample is not simple random because some samples are not possible, such as a sample containing the first 50 students on the list. or B) Yes. The sample is simple random because all samples of 50 students have the same chance of being selected.

B) Yes. The sample is simple random because all samples of 50 students have the same chance of being selected.

(Using the frequency distribution from problem 8, find the class midpoint for class) 1-5. A) 5.0 B) 2.5 C) 3.0 D) 3.5

C) 3.0 How? (1+5)/2= 3

(Determine which of the four levels of measurement is most appropriate). 1) Salaries of college professors. A) Interval B) Nominal C) Ratio D) Ordinal

C) Ratio (zero is the natural starting point)

Which value of correlation coefficient r indicates strong negative correlation? A) - 0.5 B) 0.8 C) 1 D) - 0.8

D) - 0.8 (close to -1)

Define: Data Item- Data Value- Frequency- Range-

Data Item - is a piece of data. Data Value - is value of a data item. Frequency - is the number of times each data value occurs. Range - is the difference between the highest value and the lowest value: R = highest value - lowest value

Define: Width- Midpoint-

Width: the difference between two consecutive lower class limits. In the previous example, the class width is 70 - 60 = 10. Midpoint = are the values in the middle of the classes. (Lower Limit + Upper Limit) / 2

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. A test score of 50.0 on a test having a mean of 69 and a standard deviation of 10. A) -1.9; not unusual B) 1.9; unusual C) 1.9; not unusual D) -1.9; unusual

z= x-x/s = 50-69/10 = 1.9 ( z < 2 )not significant A) -1.9; not unusual