# Data Gathering Techniques, Frequency etc.

Final Project

The Final Project is due no later than the end of Unit 9.

These are the Final Project questions:

Problem 1)

A book inventory record contains the following information:

a) Title: More Mysteries

b) Author: Roger Mortimer

c) Date of publication: 1998

d) List price: $25.00

e) Number in stock: 6

For the information (a) to (e) list the highest level of measurement as ratio, interval, ordinal, or nominal.

Problem 2)

What technique for gathering data (sampling, experiment, simulation or census) do you think was used in each of the following studies?

a) A computer program was used to model global weather patterns and to produce long-range weather forecasts for a rural agricultural region.

b) A random sample of 1,000 residents of a major metropolitan area was surveyed to determine the level of support for a new sports complex among all residents of the area.

c) To determine the effect of a new fertilizer on productivity of tomato plants one group of plants is treated with the new fertilizer while a second group is grown without such treatment. The number of ripe tomatoes produced by each group is counted.

d) A study was done regarding the number of home runs scored by major league baseball teams playing at altitudes over 5,000 feet. Data for all major league baseball games played at this altitude was used in the study.

Problem 3)

To determine monthly rental prices of apartment units in San Francisco Bay area, samples were constructed in the following ways. Identify the technique used to produce each sample. (cluster, convenience, random, stratified, systematic):

a) Number all the units in the area and use a random number table to select the apartments to include in the sample.

b) Classify the apartment units according to the number of bedrooms and then take a random sample from each of the classes.

c) Classify the apartments according to zip code and take a random sample from each of the zip code regions.

d) Look in the newspaper and choose the first apartments you find that list rents.

Problem 4)

The golf scores for the 20 members of a country club were as follows:

81, 76, 107, 95, 119, 92, 83, 74, 108, 88

95, 74, 83, 76, 97, 82, 79, 91, 93, 89

Create a relative frequency histogram using ten-point intervals to show the distribution of the scores.

Problem 5)

The data below show the average daily high temperature for Chicago, Illinois, for twelve recent spring and summer months. Construct a stem-and-leaf diagram for the data:

64, 61, 57, 68, 78, 75, 50, 83, 71, 58, 62, 80

Problem 6)

Black Hole Pizza Parlor instructs its cooks to put a "handful" of cheese on each large pizza. A random sample of six such handfuls were weighed. The weights to the nearest ounce were:

3 2 3 4 3 5

a) Find the mode, the median and the mean weight of the handfuls of cheese.

b) Find the range and the stand deviation of the weights

Problem 7)

The cost of one serving of peanut butter (in cents) for a random sample of 19 jars of peanut butter was found to be:

22 27 32 26 26 19 16

26 14 21 20 21 20 17

12 32 17 9 16

a) Give the five-number summary (low, Q1, median, Q3, high)

b) Calculate the IQR.

Problem 8)

In a random sample of eight military contracts involving cost overruns, the following information was obtained. x = big price of the contract (in millions of dollars) and y = cost of overrun (expressed as a percent of the bid price).

x 6 10 3 5 9 18 16 21

y 31 25 39 35 29 12 17 8

a) Draw the scatter diagram for this data.

b) Find the slope, b, and the intercept, a, for the least-squares line. Write the equation of the least-squares line.

c) Graph the least-squares line on your scatter diagram.

d) If an overrun contract was bid at 12 million dollars, what does the least-squares line predict for the cost of overrun (as a percent of bid price)?

Problem 9)

Mary Sue wants to know if there is a connection between attendance at craft fairs and the number of exhibitors who have booths at the fair. For a random sample of seven local craft fairs, she chose a random day of the fair and recorded the number of exhibitors. In the data below, x represents the number of exhibitors and y represents the attendance in hundreds of people.

x 35 55 75 95 100 135 150

y 1.2 2.1 4.2 5.4 5.8 6.2 9.5

a) Draw the scatter diagram for the data.

b) Calculate the sample correlation coefficient, r.

c) Calculate the coefficient of determination, r2.

d) What does the coefficient of determination tell you about the variation in attendance and the variation in the number of exhibitors?

Problem 10)

You roll two fair dice, one red and one green.

a) What is the probability of getting a number less than 5 on both?

b) What is the probability of getting a sum of 9 on the two dice?

c) What is the probability of getting a 5 on both?

Problem 11)

An urn contains 8 balls identical in every respect except color. There are 4 blue balls, 3 red balls, and 1 white ball.

a) If you draw one ball from the urn what is the probability that it is blue or white?

b) If you draw two balls without replacing the first one, what is the probability that the first ball is red and the second ball is white?

c) If you draw two balls without replacing the first one, what is the probability that one ball is red and the other is white?

Problem 12)

Evaluate:

a) P6,4

b) C7,2

c) P4,4

d) C9,0

Problem 13)

Laura is training for a week-long mountain cycling tour. She has 12 short hilly routes from which to choose mid-week rides.

a) How many ways can she choose 4 different rides from the list for the first week's training if order matters?

b) How many ways can she choose 4 different rides if order does not matter?

c) If she has chosen the first weeks rides, how many ways can she choose four more different rides for the second week? Assume that order does not matter.

Problem 14)

Identify each of the random variables as continuous or discrete.

a) Speed of an automobile

b) The number of doughnuts left in the pantry

c) The air temperature of a public park

d) The weight of a professional wrestler

e) The number of restaurant patrons

Problem 15)

Richard has just been given a ten-question multiple choice test in his history class. Each question has five answers only one of which is correct. Since Richard has not attended class recently, he does not know any of the answers. Assume that Richard guesses randomly on all ten questions.

a) Find the probability that he will answer all 10 questions correctly.

b) Find the probability that he will answer 5 or more questions correctly.

c) Find the probability that he will answer none of the questions correctly.

d) Find the probability that he will answer at least 3 questions correctly.

Problem 16)

Long-term history has shown that 65% of all elected offices in a rural county have been won by Republican candidates. This year there are 5 offices up for public election in the county Let r be the number of public offices won by Republicans.

a) Find P(r) for r=0,1,2,3,4, and 5

b) Make a histogram for the r probability distribution.

c) What is the expected number of Republicans who will win office in the coming election?

d) What is the standard deviation of r?

Problem 17)

Lewis earned 85 on his biology midterm and 81 on his history midterm. In the biology class the mean score was 79 with standard deviation 5. In the history class the mean score was 76 with standard deviation 3.

a) Convert each midterm score to a standard z score.

b) On which test did he do better compared to the rest of the class?

Problem 18)

Let x be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that x has an approximately normal distribution with mean μ = 6.8 hours and standard deviation σ = 2.1 hours.

Convert each of the following x intervals to standardized z intervals:

a) x ≤ 7.5

b) 5 ≤ x ≤ 8

c) x ≥ 4

Convert each of the following z intervals to raw score x intervals:

d) z ≥ -2

e) 0 ≤ z ≤ 2

f) z ≤ 3

Problem 19)

Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:

a) What is the probability that the drug will be effective for 2 hours or less?

b) What is the probability that the drug will be effective for 1 hour or less?

c) What is the probability that the drug will be effective for 3 hours or more?

Problem 20)

Roger has read a report that the weights of adult mail Siberian tigers have a distribution which is approximately normal with mean μ = 390 lb and σ = 65 lb.

a) Find the probability that an individual male Siberian tiger will weigh more than 450 lb.

b Find the probability that a random sample of 4 male Siberian tigers will have a sample mean weight more than 450 lb.

Problem 21)

A biologist has found the average weight of 12 randomly selected mud turtles to be 8.7 lb with standard deviation 3.6 lb. Find a 90% confidence interval for the population mean weight of all such turtles.

Problem 22)

How tall are college hockey players? The average height has been 68.3 inches. A random sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with σ = 0.9 inch. Does this indicate that the population mean height is different from 68.3 inches? Use 5% level of significance.

a) State the null and the alternate hypothesis.

b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical value(s).

c) Compute the z or t value of the sample test statistic.

d) Find the P value or an interval containing the P value for the sample test statistic.

e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level. Explain your conclusion in the context of the problem.

Problem 23)

Recently the national average yield on municipal bonds has been μ = 4.19%. A random sample of 16 Arizona municipal bonds gave an average yield of 5.11% with a sample standard deviation s = 1.15%. Does this indicate that the population mean yield for all Arizona municipal bonds is greater than the national average? Use α = 0.05. Assume x is normally distributed.

a) State the null and the alternate hypothesis.

b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical value(s).

c) Compute the z or t value of the sample test statistic.

d) Find the P value or an interval containing the P value for the sample test statistic.

e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level. Explain your conclusion in the context of the problem.

#### Solution Preview

Final Project

The Final Project is due no later than the end of Unit 9.

These are the Final Project questions:

Problem 1)

A book inventory record contains the following information:

a) Title: More Mysteries

b) Author: Roger Mortimer

c) Date of publication: 1998

d) List price: $25.00

e) Number in stock: 6

For the information (a) to (e) list the highest level of measurement as ratio, interval, ordinal, or nominal.

a) Nominal

b) Nominal

c) Interval

d) Ratio

e) Ratio

Problem 2)

What technique for gathering data (sampling, experiment, simulation or census) do you think was used in each of the following studies?

a) A computer program was used to model global weather patterns and to produce long-range weather forecasts for a rural agricultural region.

Simulation

b) A random sample of 1,000 residents of a major metropolitan area was surveyed to determine the level of support for a new sports complex among all residents of the area.

Census

c) To determine the effect of a new fertilizer on productivity of tomato plants one group of plants is treated with the new fertilizer while a second group is grown without such treatment. The number of ripe tomatoes produced by each group is counted.

Experiment

d) A study was done regarding the number of home runs scored by major league baseball teams playing at altitudes over 5,000 feet. Data for all major league baseball games played at this altitude was used in the study.

Sampling

Problem 3)

To determine monthly rental prices of apartment units in San Francisco Bay area, samples were constructed in the following ways. Identify the technique used to produce each sample. (cluster, convenience, random, stratified, systematic):

a) Number all the units in the area and use a random number table to select the apartments to include in the sample.

Systematic

b) Classify the apartment units according to the number of bedrooms and then take a random sample from each of the classes.

Cluster

c) Classify the apartments according to zip code and take a random sample from each of the zip code regions.

stratified

d) Look in the newspaper and choose the first apartments you find that list rents.

Convenience

Problem 4)

The golf scores for the 20 members of a country club were as follows:

81, 76, 107, 95, 119, 92, 83, 74, 108, 88, 95, 74, 83, 76, 97, 82, 79, 91, 93, 89

Create a relative frequency histogram using ten-point intervals to show the distribution of the scores.

Problem 5)

The data below show the average daily high temperature for Chicago, Illinois, for twelve recent spring and summer months. Construct a stem-and-leaf diagram for the data:

64, 61, 57, 68, 78, 75, 50, 83, 71, 58, 62, 80

Stem Leaf

5 0 7 8

6 1 2 4 8

7 1 5 8

8 0 3

Problem 6)

Black Hole Pizza Parlor instructs its cooks to put a "handful" of cheese on each large pizza. A random sample of six such handfuls were weighed. The weights to the nearest ounce were:

3 2 3 4 3 5

a) Find the mode, the median and the mean weight of the handfuls of cheese.

Mode: 3, median: 3, mean: 3.3333

b) Find the range and the stand deviation of the weights

Range: 3, standard deviation: 1.0328

Problem 7)

The cost of one serving of peanut butter (in cents) for a random sample of 19 jars of peanut butter was found to be:

22 27 32 26 26 19 16 26 14 21 20 21 20 17 12 32 17 9 16

a) Give the five-number summary (low, Q1, median, Q3, high)

low : 9, max: 32, Q1: 16.25 median: 20, Q3: 26

b) Calculate the IQR=Q3-Q1=26-16.25=9.75

Problem 8)

In a random sample of eight military contracts involving ...

#### Solution Summary

The solution examines data gathering techniques. Frequency of data is analyzed.