07 Jan 7DD. Regression notation

MATH221 Statistics for Decision Making

Week 1 Homework

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

Homework Help:

1DA. Population/parameter/sample/statistic/inferential/descriptive (Links to an external site.) (DOCX)

Parameter

Sample

Population

Statistic

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

Homework Help:

1DA. Population/parameter/sample/statistic/inferential/descriptive (Links to an external site.) (DOCX)

Population

Sample

Statistic

Parameter

Question 3 The chances of winning the Maryland lottery are one chance in twenty-two million. The probability would be considered an example of:

Homework Help:

1DA. Population/parameter/sample/statistic/inferential/descriptive (Links to an external site.) (DOCX)

Experiment design

A sample

Inferential statistics

Descriptive statistics

Question 4 The ages of 20 first graders would be considered:

Homework Help:

1DB. Qualitative/quantitative/nominal/ordinal/interval/ratio (Links to an external site.) (DOCX)

Qualitative data

Interval data

Nominal data

Quantitative data

Question 5

Marriage status (married, single, etc.) of the faculty at a university would be considered:

Homework Help:

1DB. Qualitative/quantitative/nominal/ordinal/interval/ratio (Links to an external site.) (DOCX)

Qualitative data

Ordinal data

Quantitative data

Ratio data

MATH221 Statistics for Decision Making

Week 2 Homework

Question 1 According to company records, the probability that a washing machine will break in the first year is 4%. This would be considered:

Homework Help:

2DA. Definition of probabilities and classical, empirical, subjective probabilities (Links to an external site.) (DOCX)

Classical probability

Subjective probability

Manufactured probability

Empirical probability

Question 2 Given the following information, find the probability that a randomly selected student will be very short. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21

Homework Help:

2DB. Probabilities from a given distribution of frequencies (Links to an external site.) (DOCX)

21.0%

28.8%

21.6%

39.4%

Question 3 Given 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

Homework Help:

2DB. Probabilities from a given distribution of frequencies (Links to an external site.) (DOCX)

60.5%

46.9%

39.5%

58.0%

Question 4 Given that there is a 22% 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?

Homework Help:

2VA: Probabilities given probability of success and 2 or more events (Links to an external site.) (0:51)

2DC. Probabilities given probability of success and 2 or more events (Links to an external site.) (DOCX)

13.4%

17.2%

1.1%

78.0%

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

Red Blue Total

Yes 15 21 36

No 38 13 51

Total 53 34 87

Homework Help:

2VB: Conditional probabilities from a table (Links to an external site.) (1:45)

15/53

36/87

15/87

53/87

MATH221 Statistics for Decision Making

Week 3 Homework

Question 1Let x represent the number of pets in pet stores. This would be considered what type of variable:

Homework Help:

3DA. Discrete versus continuous variables (Links to an external site.) (DOCX)

Discrete

Nonsensical

Lagging

Continuous

Question 2Let x represent the height of corn in Oklahoma. This would be considered what type of variable:

Homework Help:

3DA. Discrete versus continuous variables (Links to an external site.) (DOCX)

Distributed

Discrete

Continuous

Inferential

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?

Homework Help:

3DB. Probabilities from a probability distribution (Links to an external site.) (DOCX)

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) 0.16

41-50 (average=43) 0.72

51 and over (average=54) 0.04

Find the mean of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

39.0

40.7

39.5

40.0

Question 5Consider the following table.

Defects in batch Probability

0 0.09

1 0.24

2 0.41

3 0.12

4 0.10

5 0.04

Find the variance of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

1.48

1.43

1.22

2.02

MATH221 Statistics for Decision Making

Week 4 Homework

Question 1 The 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 5 minutes to select a shoe purchase. Is this outcome unusual?

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.) (DOCX)

Probability is 0.03, which is usual as it is not less than 5%

Probability is 0.97, which is unusual as it is greater than 5%

Probability is 0.03, which is unusual as it is less than 5%

Probability is 0.97, which is usual as it is greater than 5%

Question 2 Monthly 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 $173, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.)(DOCX)

Probability is 0.04, which is unusual as it is not less than 5%

Probability is 0.04, which is usual as it is less than 5%

Probability is 0.04, which is unusual as it is less than 5%

Probability is 0.04, which is usual as it is not less than 5%

Question 3 In 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.

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.)(DOCX)

0.70

Less than 1%

0.40

0.30

Question 4 A 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 0.50mm. Would this outcome warrant a refund (meaning that it would be unusual)?

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.)(DOCX)

Probability of 0.09 and would not warrant a refund

Probability of 0.09 and would warrant a refund

Probability of 0.91 and would warrant a refund

Probability of 0.91 and would not warrant a refund

Question 5 A 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 1.04 minutes.

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.)(DOCX)

0.007

0.501

0.993

0.071

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?

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

5DA. Concept and meaning of confidence intervals (Links to an external site.) (DOCX)

(21.78, 22.60)

(19.24, 24.14)

(20.71, 22.67)

(20.86, 22.52)

Question 2 If 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?

Homework Help:

5DB. Finding margin of error from given confidence interval (Links to an external site.) (DOCX)

43.83

18.14

4.54

9.07

Question 3 If a car manufacturer wanted lug nuts that fit nearly all the time, what characteristics would be better?

Homework Help:

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

narrow confidence interval at low confidence level

wide confidence interval with high confidence level

wide confidence interval with low confidence level

narrow confidence interval at high confidence level

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

Homework Help:

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

large standard deviation

large mean

small sample size

small standard deviation

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

Homework Help:

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

a small margin of error

a large standard deviation

a large sample size

a large mean

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 more than 63 months. Write the null and alternative hypotheses and note which is the claim.

Homework Help:

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)

Ho: ? ? 63, Ha: ? < 63 (claim) Ho: ? = 63 (claim), Ha: ? ? 63 Ho: ? ? 63, Ha: ? > 63 (claim)

Ho: ? > 63 (claim), Ha: ? ? 63

Question 2A business claims that the mean time that customers wait for service is at most 5.9 minutes. Write the null and alternative hypotheses and note which is the claim.

Homework Help:

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)

Ho: ? > 5.9 (claim), Ha: ? > 5.9

Ho: ? ? 5.9, Ha: ? ? 5.9 (claim)

Ho: ? ? 5.9 (claim), Ha: ? > 5.9

Ho: ? > 5.9, Ha: ? ? 5.9 (claim)

Question 3An amusement park claims that the average daily attendance is at least 20,000. Write the null and alternative hypotheses and note which is the claim.

Homework Help:

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)

Ho: ? > 20000 (claim), Ha: ? = 20000

Ho: ? ? 20000, Ha: ? > 20000 (claim)

Ho: ? ? 20000 (claim), Ha: ? < 20000 Ho: ? = 20000, Ha: ? ? 20000 (claim) Question 4A transportation organization claims that the mean travel time between two destinations is about 23 minutes. Write the null and alternative hypotheses and note which is the claim. Homework Help: 6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX) Ho: ? > 23, Ha: ? ? 23 (claim)

Ho: ? ? 23, Ha: ? = 23 (claim)

Ho: ? = 23 (claim), Ha: ? ? 23

Ho: ? = 23 (claim), Ha: ? ? 23

Question 5If the null hypothesis is not rejected when it is false, this is called __________.

Homework Help:

6DB. Type I and type II errors (Links to an external site.) (DOCX)

the Empirical Rule

an alternative hypothesis

a type I error

a type II error

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?

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

Dependent variable decreases

Dependent variable increases

Cannot determine from information given

Dependent variable would remain the same

Question 2What does the variable r represent?

Homework Help:

7DB. Correlation coefficient and coefficient of determination, notation and meanings (Links to an external site.) (PDF)

The coefficient of determination

The sample correlation coefficient

The population correlation coefficient

The critical value for the correlation coefficient

Question 3A golfer wants to determine if the type of driver she uses each year can be used to predict the amount of improvement in her game. Which variable would be the explanatory variable?

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

7DC. Explanatory and response variables (Links to an external site.) (PDF)

The number of holes she plays

The improvement in her game

The type of driver

The rating of the golfer

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

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

Below 0

To the left of 0

Cannot determine

To the right of 0

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

Homework Help:

7DD. Regression notation of m, b, y1, x1, yi, xi, means of variables, estimates of variables (Links to an external site.) (PDF)

y1

b

m

yi