Devry MATH221 Statistics for Decision Making Week Homeworks

Devry MATH221 Statistics for Decision Making Week Homeworks

Week 1 Homework

Question 1The age of every fourth person entering a department store. The selected individuals would be considered a:

Statistic

Parameter

Population

Correct!

Sample

Question 2 In a survey of 1000 adults, 34% found they prefer charcoal to gas grills. The 1000 would be considered a:

Sample

Population

Parameter

Statistic

The article I selected is called “Selective immunoglobulin A deficiency in children with diabetes mellitus: Data from a medical center in Ukraine.” This article reports a study done in western Ukraine. The goal of the study was to estimate the prevalence of selective immunoglobulin A deficiency (SIgAD) among children with type 1 diabetes mellitus (DM). (Selective IgA deficiency is an immune system condition in which you lack or don’t have enough immunoglobulin A (IgA), a protein that fights infection) (MayoClinic.org). According to this article, SIgAD is one of the most common primary immunodeficiencies, and its prevalence ranges from 1:300 to 1:3000 depending o the population. SIgAD is diagnosed in children older than four years with serum IgA below 7mg/dL, with normal immunoglobulins G (IgG) and M(IgM) and other causes of hypogammaglobulinemia and T cells defects ruled out. In addition, the article also reports that this deficiency is a heterogeneous condition with a multifactorial mechanism and its pathogenesis is not completely understood and typically is associated with defects in B cells failing to produce IgA and T cell abnormalities and cytokine abnormalities also may play a role on this deficiency.

Question 3Inferential statistics is when sample data is used to:

Influence a decision maker

Calculate a mean

Say something about the population

Determine when an event is most likely to occur

Question 4The milligrams of tar in 30 cigarettes would be considered:

Interval data

Ratio data

Ordinal data

Nominal data

Question 5If a data set included the color of cars in a parking lot, those data would be considered:

Quantitative data

Ratio data

Qualitative data

Interval data

Question 6The amount of fat in grams in 58 cookies would be considered:

Interval data

Nominal data

Ordinal data

Ratio data

Question 7Five statistics classes out of 20 are selected and all the students in the selected classes are interviewed. This sampling technique is called:

Cluster

Convenience

Stratified

Random

Question 8A personnel director at a large company would like to determine whether the company cafeteria is widely used by employees. She calls each employee and asks them whether they usually bring their own lunch, eat at the company cafeteria, or go out for lunch. This study design would be considered:

Survey

Experimental

Observational

Simulation

Question 9Which of the following would be the mean of this data set: 5, 28, 12, 56, 4, 2, 30, 21

17.06

16.50

18.24

19.75

Question 10Which of the following would be the standard deviation of this population data set: 67, 54, 30, 77, 92, 41, 75, 81

21.226

64.625

19.855

517.000

Question 11Which of the following would be the variance of this population data set: 3, 6, 8, 9, 4, 5, 7, 1, 9, 7, 15, 4, 3, 1

25.73

13.00

3.74

14.00

Question 12What is the relationship between variance and standard deviation?

Variance is double the standard deviation

Standard deviation is double the variance

Standard deviation is the square of the variance

Variance is the square of the standard deviation

Question 13If data set A has a larger standard deviation than data set B, what would be different about their distributions?

Data set A would have flatter distribution with more data in each tail

Data set A would have a larger mean

Data set A would have more data near the center of the distribution

Data set A would have most of its data to one side of the distribution

Question 14In a normally distributed data set a mean of 55 where 99.7% of the data fall between 47.5 and 62.5, what would be the standard deviation of that data set?

2.5

5.0

7.5

5.7

Question 15Which of the following data sets would you expect to have the highest mean?

Height of pit bulls (in inches)

Prices of used cars (in dollars)

Ages of kids in a preschool program (in years)

Speed of cars during a professional car race (in mph)

Question 16

Which data outcome of the number of customers in line would best support opening another cash register?

High mean with small standard deviation

Low mean with high standard deviation

High mean with high standard deviation

Low mean with small standard deviation

Question 17In manufacturing, convenience sampling could be used to determine if the machines are operating correctly. Which of the following best describes this type of sampling?

Products are put into groups and some are randomly selected from each group

Every 10th product in the line is selected

Products are put into groups and all are included from several randomly selected groups

Samples are randomly selected throughout the day

Question 18A graph shows a line connecting the tops of vertical bars with the number of data points on the y-axis and groups on the x-axis. This graphic is most likely to be:

A dot plot

A frequency histogram

A frequency polygon

A stem-leaf plot

Question 19Match the terms and their definitions

Vertical bar chart that shows frequency on the y-axis

A sample where the population is divided into groups and several groups are randomly selected from all from those selected groups are sampled

Collection of all counts that are of interest

A subset or part of a population

A sample where the population is divided into groups and several are randomly sampled form each group

Consists of attributes, labels, or nonnumerical entries

Question 20Match the terms and their definitions

The most frequent number appearing in a dataset

The average

The percentage of data that falls within 1, 2, or 3 standard deviations of the mean in a symmetrical, bell-shaped distribution

The square root of the variance

Show how far a particular data point is from the mean in terms of the number of standard deviations

MATH221 Statistics for Decision Making

Week 2 Homework

Question 1A student believes that there is a 90% probability of getting an A on the next test. This would be considered:

Empirical probability

Manufactured probability

Subjective probability

Classical probability

Question 2Given the following information, find the probability that a randomly selected student will be tall, but not very tall. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21

50.5%

39.4%

10.1%

49.5%

Question 3Given the following information, find the probability that a randomly selected dog will be a golden retriever or a poodle. Number of dogs who are poodles: 31, golden retrievers: 58, beagles: 20, pugs: 38

46.9%

58.0%

39.5%

60.5%

Question 4Given that there is a 28% chance it will rain on any day, what is the probability that it will rain on the first day and be clear (not rain) on the next two days?

20.2%

14.5%

5.6%

34.7%

Question 5Consider the following table. What is the probability of blue?

Red Blue Green Total

Yes 33 44 14 91

No 18 5 28 51

Total 51 49 42 142

44/49

91/142

49/142

51/142

Question 6Consider the following table. What is probability of yes, given green?

Red Blue Green Total

Yes 33 44 14 91

No 18 5 28 51

Total 51 49 42 142

14/91

14/42

51/142

42/142

Question 7A card is randomly selected from a standard deck of 52 cards. What is P(heart)?

13/52

4/52

1/52

26/52

Question 8In a sample of 500 customers, 140 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?

Homework Help:

2VE: Probabilities of drawing several from many without replacement (Links to an external site.) (1:35)

2DE. Probabilities of drawing several from many without replacement (Links to an external site.) (DOCX)

14.00%

7.80%

28.84%

7.84%

Question 9In a sample of 587 customers, 308 say they are happy with the service. If you select three customers without replacement for a commercial, what is the probability they will all say they are happy with the service?

52.47%

14.38%

14.45%

27.53%

Question 10One event is a father being right handed. The other event is that his daughter is right handed. How would you classify these events?

Independent

Dependent

MATH221 Statistics for Decision Making

Week 3 Homework

Question 1Let x represent the number of cars in a parking lot. This would be considered what type of variable:

Discrete

Nonsensical

Continuous

Lagging

Question 2 Let x represent the inches of rain on crops in Akron, Ohio. This would be considered what type of variable:

Continuous

Discrete

Inferential

Distributed

Question 3Consider the following table.

Age Group Frequency

18-29 9831

30-39 7845

40-49 6869

50-59 6323

60-69 5410

70 and over 5279

If you created the probability distribution for these data, what would be the probability of 40-49?

42.5%

23.7%

18.9%

16.5%

Question 4Consider the following table.

Weekly hours worked Probability

1-30 (average=23) 0.08

31-40 (average=36) 0.10

41-50 (average=43) 0.74

51 and over (average=54) 0.08

Find the mean of this variable.

39.0

31.8

41.6

25.2

Question 5Consider the following table.

Defects in batch Probability

0 0.28

1 0.35

2 0.16

3 0.09

4 0.10

5 0.02

Find the variance of this variable.

0.85

1.44

1.35

1.83

Question 6Consider the following table.

Defects in batch Probability

2 0.18

3 0.29

4 0.18

5 0.14

6 0.11

7 0.10

Find the standard deviation of this variable.

2.49

4.01

1.58

1.52

Question 7The standard deviation of samples from supplier A is 0.0841, while the standard deviation of samples from supplier B is 0.0926. Which supplier would you be likely to choose based on these data and why?

Supplier A, as their standard deviation is higher and, thus easier to fit into our production line

Supplier A, as their standard deviation is lower and, thus, easier to fit into our production line

Supplier B, as their standard deviation is lower and, thus, easier to fit into our production line

Supplier B, as their standard deviation is higher and, thus, easier to fit into our production line

Question 8Ten fourth graders are randomly selected. The random variable represents the number of fourth graders who own a smartphone. For this to be a binomial experiment, what assumption needs to be made?

The probability of being selected is the same for all fourth graders

The probability of owning a smartphone is the same for all fourth graders

All ten selected fourth graders are the same age

The probability of being a fourth grader is the same for all those selected

Question 9A survey found that 39% of all gamers play video games on their smartphones. Ten frequent gamers are randomly selected. The random variable represents the number of frequent games who play video games on their smartphones. What is the value of n?

0.10

x, the counter

0.39

Question 10

Forty-four percent of US adults have little confidence in their cars. You randomly select twelve US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly six and then find the probability that it is (2) more than 7.

(1) 0.207 (2) 0.901

(1) 0.793 (2) 0.099

(1) 0.762 (2) 0.901

(1) 0.207 (2) 0.099

MATH221 Statistics for Decision Making

Week 4 Homework

Question 1The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?

Probability is 0.09, which is unusual as it is less than 5%

Probability is 0.91, which is usual as it is greater than 5%

Probability is 0.09, which is usual as it is not less than 5%

Probability is 0.91, which is unusual as it is greater than 5%

Question 2Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. Find the probability that a randomly selected bill will have an amount greater than $165, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?

Probability is 0.06, which is unusual as it is not less than 5%

Probability is 0.06, which is usual as it is not less than 5%

Probability is 0.94, which is usual as it is greater than 5%

Probability is 0.94, which is unusual as it is greater than 5%

Question 3In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

0.40

Less than 1%

0.70

0.30

Question 4A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.70mm. Would this outcome warrant a refund (meaning that it would be unusual)?

Probability of 0.79 and would not warrant a refund

Probability of 0.79 and would warrant a refund

Probability of 0.21 and would not warrant a refund

Probability of 0.21 and would warrant a refund

Question 5A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 7.45 minutes with a standard deviation of 2.81 minutes.

0.818

0.636

0.182

0.018

Question 6In an agricultural study, the average amount of corn yield is normally distributed with a mean of 185.2 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1100 acres, about how many would be expected to yield more than 190 bushels of corn per acre?

503 acres

419 acres

461 acres

639 acres

Question 7On average, the parts from a supplier have a mean of 31.8 inches and a standard deviation of 2.4 inches. Find the probability that a randomly selected part from this supplier will have a value between 27.0 and 36.6 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?

Probability is 0.95, which is consistent with the Empirical Rule

Probability is 0.02, which is inconsistent with the Empirical Rule

Probability is 0.98, which is inconsistent with the Empirical Rule

Probability is 0.95, which is inconsistent with the Empirical Rule

Question 8A process is normally distributed with a mean of 10.6 hits per minute and a standard deviation of 0.49 hits. If a randomly selected minute has 11.8 hits, would the process be considered in control or out of control?

In control as this one data point is not more than three standard deviations from the mean

In control as only one data point would be outside the allowable range

Out of control as this one data point is more than three standard deviations from the mean

Out of control as this one data point is more than two standard deviations from the mean

Question 9The candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 grams and a standard deviation of 0.9 grams. The company takes readings of every 10th bar off the production line. The reading points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 19.4. Is the process in control or out of control and why?

It is out of control as two of these data points are more than 2 standard deviations from the mean

It is out of control as the values jump above and below the mean

It is out of control as at least two of three consecutive data points are more than 2 standard deviations from the mean

It is out of control as one of these data points is more than 3 standard deviations from the mean

Question 10The toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, what warranty should be provided so that the company is replacing at most 5% of their toasters sold?

5.9 years

7.3 years

4.6 years

4.3 years

MATH221 Statistics for Decision Making

Week 5 Homework

Question 1 From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.69 with a population standard deviation of 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues?

(19.24, 24.14)

(20.71, 22.67)

(21.78, 22.60)

(20.86, 22.52)

Question 2If a confidence interval is given from 43.83 up to 61.97 and the mean is known to be 52.90, what is the margin of error?

4.54

9.07

18.14

43.83

Question 3If a computer manufacturer needed a supplier that could produce parts that were very precise, what characteristics would be better?

wide confidence interval with high confidence level

narrow confidence interval at high confidence level

narrow confidence interval at low confidence level

wide confidence interval with low confidence level

Question 4Which of the following are most likely to lead to a wide confidence interval?

large sample size

small standard deviation

large mean

large standard deviation

Question 5If you were designing a study that would benefit from a narrow range of data points, you would want the input variable to have:

a small mean

a small sample size

a large standard deviation

a small margin of error

Question 6The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 57.06. What should be done about the production line?

Keep the line operating as it is outside the confidence interval

Stop the line as it is close to the confidence interval

Keep the line operating as it is close to the confidence interval

Stop the line as it is outside the confidence interval

Question 7In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 29.7 degrees and the population standard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer?

(29.16, 30.24)

(27.00, 32.4)

(24.30, 35.10)

(31.36, 32.44)

Question 8What is the 99% confidence interval for a sample of 52 seat belts that have a mean length of 85.6 inches long and a population standard deviation of 2.9 inches?

(84.4, 86.8)

(83.1, 88.1)

(84.6, 86.6)

(84.7, 86.5)

Question 9If two samples A and B had the same mean and sample size, but sample A had a larger standard deviation, which sample would have the wider 95% confidence interval?

Sample A as it has the larger sample

Sample B as it has the smaller sample

Sample B as its sample is more disperse

Sample A as its sample is more disperse

Question 10Why might a company use a lower confidence interval, such as 80%, rather than a high confidence interval, such as 99%?

It is cheaper as the sample size needs to be larger

It is faster as the sample size can be smaller

It is faster as more samples can be collected in a shorter time

It is cheaper as more samples can be collected

MATH221 Statistics for Decision Making

Week 6 Homework

Question 1A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 36 months. Write the null and alternative hypotheses and note which is the claim.

Ho: μ ≤ 36, Ha: μ > 36 (claim)

Ho: μ > 36, Ha: μ ≤ 36 (claim)

Ho: μ ≤ 36 (claim), Ha: μ > 36

Ho: μ = 36 (claim), Ha: μ ≥ 36

Question 2A business claims that the mean time that customers wait for service is at most 9.2 minutes. Write the null and alternative hypotheses and note which is the claim.

Ho: μ ≥ 9.2, Ha: μ ≤ 9.2 (claim)

Ho: μ > 9.2, Ha: μ ≤ 9.2 (claim)

Ho: μ > 9.2 (claim), Ha: μ > 9.2

Ho: μ ≤ 9.2 (claim), Ha: μ > 9.2

Question 3An amusement park claims that the average daily attendance is at least 15,000. Write the null and alternative hypotheses and note which is the claim.

>Ho: μ ≥ 15000 (claim), Ha: μ < 15000

Ho: μ = 15000, Ha: μ ≤ 15000 (claim)

Ho: μ ≤ 15000, Ha: μ > 15000 (claim)

Ho: μ > 15000 (claim), Ha: μ = 15000

Question 4A transportation organization claims that the mean travel time between two destinations is about 12 minutes. Write the null and alternative hypotheses and note which is the claim.

Ho: μ = 12 (claim), Ha: μ ≤ 12

Ho: μ = 12 (claim), Ha: μ ≠ 12

Ho: μ > 12, Ha: μ ≤ 12 (claim)

Ho: μ ≠ 12, Ha: μ = 12 (claim)

Question 5 Type I and type II errors occur because of what issue within the hypothesis testing process?

The population is not a representative subset of the sample

The sample mean is different than the population mean

The sample taken is not representative of the population

The math calculations were done incorrectly

Question 6A scientist claims that the mean gestation period for a fox is 51.5 weeks. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted?

There is not enough evidence to support the scientist’s claim that the gestation period is more than 51.5 weeks

There is not enough evidence to support the scientist’s claim that the gestation period is 51.5 weeks

There is enough evidence to support the scientist’s claim that the gestation period is 51.5 weeks

The evidence indicates that the gestation period is less than 51.5 weeks

Question 7A marketing organization claims that more than 10% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?

There is sufficient evidence to support the claim that less than 10% of the employees are paid minimum wage

There is sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage

There is not sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage

There is not sufficient evidence to support the claim that 10% of the employees are paid minimum wage

Question 8A sprinkler manufacturer claims that the average activating temperatures is at most 131 degrees. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133 degrees. Assume the population standard deviation is 3.3 degrees. Find the standardized test statistic and the corresponding p-value.

z-test statistic = 3.43, p-value = 0.0006

z-test statistic = -3.43, p-value = 0.0006

z-test statistic = -3.43, p-value = 0.0003

z-test statistic = 3.43, p-value = 0.0003

Question 9A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 6.8 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour of 7.6 seconds. Assume the population standard deviation is 2.3 seconds. Find the standardized test statistic and the corresponding p-value.

z-test statistic = -1.998, p-value = 0.023

z-test statistic = -1.998, p-value = 0.046

z-test statistic = 1.998, p-value = 0.046

z-test statistic = 1.998, p-value = 0.023

Question 10A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 41.5 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the test statistic?

Claim is alternative, fail to reject the null and support claim as test statistic (2.05) is not in the rejection region defined by the critical value (1.64)

Claim is alternative, reject the null and support claim as test statistic (2.05) is in the rejection region defined by the critical value (1.64)

Claim is null, fail to reject the null and reject claim as test statistic (2.05) is not in the rejection region defined by the critical value (1.96)

Claim is null, reject the null and reject claim as test statistic (2.05) is in the rejection region defined by the critical value (1.96)

MATH221 Statistics for Decision Making

Week 7 Homework

Question 1Two variables have a negative non-linear correlation. Does the dependent variable increase or decrease as the independent variable increases?

Dependent variable decreases

Dependent variable increases

Cannot determine from information given

Dependent variable would remain the same

Question 2What does the variable ρ represent?

The critical value for the correlation coefficient

The coefficient of determination

The sample correlation coefficient

The population correlation coefficient

Question 3A baseball player wants to determine if the type of bat he uses each year can be used to predict the amount of improvement in his game. Which variable would be the response variable?

The improvement in his game

The number of times he bats

The type of bat

The baseball player

Question 4Two variables have a negative linear correlation. Where would the y-intercept of the regression line be located on the y-axis?

To the right of 0

To the left of 0

Cannot determine

Below 0

Question 5A value of the dependent variable that corresponds to the value of xi would be given the notation of:

Question 6What would be the notation for an estimate of y for a specific value of x?

Question 7Which of the following graphs displays the regression equation ?=-0.91x + 11.97

Scatter plot generally from lower left to upper right where y-intercept is estimated to be around 6

Scatter plot generally from upper left to lower right where y-intercept is estimated to be around 7

Scatter plot generally from lower left to upper right where y-intercept is estimated to be around 30

Scatter plot generally from upper left to lower right where y-intercept is estimated to be around 12

Question 8Find the regression equation for the following data set

x 123 146 127 161 122 174 134 155

y 80 51 59 41 44 59 51 63

0.13x – 74.50

-0.13x+74.50

74.50x – 0.13

cannot be determined

Question 9A data set whose original x values ranged from 41 through 78 was used to generate a regression equation of ?=5.3x – 21.9. Use the regression equation to predict the value of y when x=70.

402.1

Meaningless result

392.9

349.1

Question 10A data set whose original x values ranged from 120 through 351 was used to generate a regression equation of ?=0.06x + 14.2. Use the regression equation to predict the value of y when x=110.

20.80

Meaningless result

-7.6

21.34