In a recent year, about two-thirds of U.S. households purchased ground coffee. Consider the annual ground coffee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distributed as a normal random variable with a mean of $75 and a standard deviation of $10.

a. Find the probability that a household spent less than $65.00.

b. Find the probability that a household spent more than $80.00.

c. What proportion of the households spent between $65.00 and $80.00?

d. 99% of the households spent less than what amount?

Show all work.

1. On a job interview you ask the employer what would the starting salary be. The interviewer says, "the average starting salary in my company will be $80,000."

You accept the job and find out your starting salary will be $30,000.

You and 6 co-workers have a starting salary of $30,000 while the CEO's son has a starting salary of $430,000! The average (mean) is $80,000.

You think this is a misuse of statistics because the employer should have used

a).a sample instead of the entire population (suspect samples)

b).a different average like the median (ambiguous average)

c). a lie detector

2.  

The mean of the grades: 100, 90, 100, 70, and 100.

is 92.

True or False

3. Match the key terms with their definitions.

a)the certainty that the observations in our sample group are accurate measures of the characteristics we set out to measure

b)a sample drawn from a population such that each and every member of the population has an equal chance of being included in the sample. Also, every sample of the same size has an equal chance of being selected.

c)being sure that our methods and presence in no way jeopardize our ability to use the random sample as a true representative of the population

d) another term for consistency

e) a convenient method of organizing raw data into a table, using classes

f) a way to display the distribution when we want to emphasize the categories' relation to the whole

1. Pie chart 2. Frequency Distribution 3. Reliability 4. External Validity 5. Internal Validity 6. Random Sample

Connor is a statistics student interested in the number of games won by each team per season during the past 12 years for a certain professional baseball league. He records the total number of wins x for each team each season and the probability of each value P(x), as shown in the table provided. Use Excel to find the mean and the standard deviation of the probability distribution. Round the mean and standard deviation to three decimal places. Number of wins, x P(x) 54 0.003 55 0.009 56 0.015 57 0.012 58 0.006 59 0.018 60 0.024 61 0.036 62 0.027 63 0.045 64 0.036 65 0.045 66 0.039 67 0.054 68 0.051 69 0.060 70 0.054 71 0.071 72 0.059 73 0.045 74 0.042 75 0.030 76 0.033 77 0.036 78 0.027 79 0.024 80 0.021 81 0.018 82 0.012 83 0.015 84 0.015 85 0.009 86 0.006 87 0.003

Problem Details:

A major beverage company needs forecasts of sales for next year. Quarterly sales data for the previous 13 years can be found in the “Beverage_Sales” worksheet of the Excel file titled Group Case #2 Data.

Requirements (You will NOT follow the PLAN-DO-REPORT algorithm. Address/answer all requirements in the order given.):

1. (2 points) Create a Time Series plot of the sales data. Briefly describe what you see in the plot.

2. (5 points) Develop a model to forecast sales for the four quarters of year 14.

3. (2 points) Forecast sales for the four quarters of year 14.

4. (4 points) Determine the MSE, MAD, MAPE for the model you developed in requirement #2. Using this information and any relevant information from the results of requirement #2, briefly discuss how accurate you think the forecasts for year 14 are.

Data:

57 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows:

Round all your answers to 4 decimal places where possible.

The mean is:

The median is:

The sample standard deviation is: _______

The first quartile is: _______

The third quartile is: _______

What percent of the respondents have at least 7 pairs of Shoes? ______%

13% of all respondents have fewer than how many pairs of Shoes? __________

A class has 8 GSIs. Each GSI tosses a coin 20 times and notes the number of heads. What is the probability that none of the GSIs gets exactly 10 heads?

Q1- Identify each of the following statistics as either descriptive or inferential. For each, give a reason to support your response.

1 The average age of students in our statistics class is 20 years old.

2 The average age of undergraduate students in the CUNY system is 20 years old.

3 Seventy-three percent of sixth-graders have cell-phones.

4 The salary of LeBron James is greater than the average salary of his teammates.

5 Eighteen of the twenty three eighth-graders in Mr. Robson's algebra class have smart phones.

6 Less than 50% of all american households have two televisions.

Q2- Classify the following data as nominal, ordinal, interval or ratio. For each, give a reason to support your response.

1   Date of high-school graduation

2   The numbers on the Lakers' jerseys

3   Ranking of the planets by distance from sun

4   Distance of planets from sun

5   Height of children in an elementary school

6   Waiting number at DMV

7   Year at high-school

8   Weight of chickens at a poultry farm

9   Longitude of stars in the night sky

10 Social security number

TThe quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 108 hours. A random sample of 81 light bulbs indicated a sample mean life of 410 hours . a. Construct a 99% confidence interval estimate for the population mean life of light bulbs in this shipment. b. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 410 hours? Explain. c. Must you assume that the population light bulb life is normally distributed? Explain. d. Suppose that the standard deviation changes to 80 hours. What are your answers in (a) and (b)?

Waiting time for checkout line at two stores of a supermarket chain were measured for a random sample of customers at each store. The chain wants to use this data to test the research (alternative) hypothesis that the mean waiting time for checkout at Store 1 is lower than that of Store 2.
Store 1 (in Seconds)
Store 2 (in Seconds)

461
264

384
308

167
266

293
224

187
244

115
178

195
279

280
289

228
253

315
223

205

197

What are the null and alternative hypothesis for this research?

What are the sample mean waiting time for checkout line and the sample standard deviation for the two stores?

Compute the test statistic t used to test the hypothesis. Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1. Use the one in Section 10.2 instead.

Compute the degree of freedom for the test statistic t.

Can the chain conclude that the mean waiting time for checkout at Store 1 is lower than that of Store 2? Use the critical-value approach and α = 0.05 to conduct the hypothesis test.

Construct a 95% confidence interval for the difference of mean waiting time for checkout line at the two stores.

To compare prices of two grocery stores in Toronto, a random sample of items that are sold in both stores were selected and their price noted in the first weekend of July 2018:

Item
Store A
Store B
Difference (Store A - Store B)

1
1.65
1.99
-0.34

2
8.70
8.49
0.21

3
0.75
0.90
-0.15

4
1.05
0.99
0.06

5
11.30
11.99
-0.69

6
7.70
7.99
-0.29

7
6.55
6.99
-0.44

8
3.70
3.59
0.11

9
8.60
8.99
-0.39

10
3.90
4.29
-0.39

What are the null and alternative hypothesis if we want to confirm that on average, prices at Store 1 is different from the prices at Store 2, that is, the difference is different from 0?

What are the sample mean difference in prices and the sample standard deviation?

Compute the test statistic t used to test the hypothesis.

Compute the degree of freedom for the test statistic t

Can we conclude that on average, prices at Store 1 is different from the prices at Store 2? Use the critical-value approach and α = 0.05 to conduct the hypothesis test.

Use the above data to construct a 95% confidence interval for the difference in prices between the two stores.

3. In a completely randomized design, 7 experimental units were used for each of the three levels of the factor. (Total: 6 marks; 2 marks each)

Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F

Treatment

Error
432076.5

Total
675643.3

Complete the ANOVA table.

Find the critical value at the 0.05 level of significance from the F table for testing whether the population means for the three levels of the factors are different.

Use the critical value approach and α = 0.05 to test whether the population means for the three levels of the factors are the same.

22 randomly selected students were asked the number of movies they watched the previous week.

The results are as follows: # of Movies 0 1 2 3 4 5 6 Frequency 4 1 1 5 6 3 2

Round all your answers to 4 decimal places where possible.

The mean is:

The median is:

The sample standard deviation is:

The first quartile is:

The third quartile is:

What percent of the respondents watched at least 2 movies the previous week? %

78% of all respondents watched fewer than how many movies the previous week?

For the following description of​ data, identify the​ W's, name the​ variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative and for any quantitative variable identify the units in which it was measured. Determine if the data comes from a designed survey or experiment. Determine if the variables are time series or​ cross-sectional.

A company surveyed a random sample of

65006500

employees in the region. One question they asked​ was, "If your employer provides you with mentoring opportunities are you likely to remain in your job for the next

tenten

​years?" They found that

580580

members of the sample said yes.

Identify the Who for this study.

A.The

65006500

employees in the region

B.The

580580

employees who answered yes

C.

All the employees in the region

D.

All people in the region

Identify the What for this study. Select all that apply.

A.

The amount an employee receives in benefits

B.

The average amount of time an employee remains at their job

C.Whether or not an employee is likely to remain at their job for the next

tenten

years

D.The average number of jobs someone goes through in a

fivefive

year period

E.The average number of jobs someone goes through in a

tenten

year period

F.Whether or not an employee is likely to remain at their job for the next

fivefive

years

Identify the When for this study.

A.Over the course of

fivefive

years

B.Within the past

tenten

years

C.

Over the course of a year

D.

This information is not given.

Identify the Where for this study.

A.

Over the phone

B.

At a hotel

C.

Online

D.

This information is not given.

Identify the Why for this study.

A.To determine the least amount of benefits to keep an employee at their job for a minimum of

tenten

years.

B.To determine how many people have been at their current job for at least

fivefive

years.

C.To determine the likelihood that someone remains at their job for the next

tenten

years given that their employer provides them with mentoring opportunities.

D.

This information is not given.

Identify the How for this study.

A.

Employers went door to door surveying residents.

B.

The company passed out a survey to be filled out during the work day.

C.

An online poll was posted on the​ company's website.

D.

This information is not given.

Specify the categorical variables for this study. Select all that apply.

A.

Amount of time at the company

B.

Gender

C.

Age

D.

Mentoring opportunities

E.Whether or not an employee is likely to remain at their job for the next

tenten

years

F.

There are no categorical variables.

Specify the quantitative variables and their units for this study. Select all that apply.

A.

Number of​ jobs; count

B.

Amount of time at the​ company; years

C.

​Age; years.

D.

Mentoring​ opportunities; count

E.

There are no quantitative variables.

Specify whether the data come from a designed survey or experiment.

Experiment

Designed survey

Are the variables time series or​ cross-sectional?

​Cross-sectional

Time series

For the following description of​ data, identify the​ W's, name the​ variables, specify for each variable whether its use indicates it should be treated as categorical or​ quantitative, and for any quantitative variable identify the units in which it was measured​ (or note that they were not​ provided). Specify whether the data come from a designed survey or experiment. Are the variables time series or​ cross-sectional? Report any concerns you have as well.

A certain horse race has been run every year since

18711871

in a city. The accompanying table shows the official race data for the first two races and two recent races.

Identify the​ "who." Choose the correct answer below.

A.

The horses that competed in the​ city's horse races

B.

The​ city's horse races

C.

Horse races

D.

This information is not given.

Identify the​ "what." Choose the correct answer below.

A.

​Year, winner,​ margin, jockey,​ winner's payoff,​ duration, track condition

B.

​Year, margin,​ winner's payoff, duration

C.

​Winner, jockey, track condition

D.

This information is not given.

Identify the​ "when." Choose the correct answer below.

A.

May

B.

18711871​-20052005

C.

18711871​,

18721872​,

20042004​,

and 20052005

D.

This information is not given.

Identify the​ "where." Choose the correct answer below.

A.

All race tracks in the state

B.

The city where the horse races took place

C.

United States

D.

This information is not given.

Identify the​ "why." Choose the correct answer below.

A.

To see if the same horse won in multiple years

B.

To maintain a list of the winners

C.

To compare the times of the winners from year to year

D.

This information is not given.

Identify the​ "how." Choose the correct answer below.

A.

A chronic better recorded the data.

B.

A random sample of races was taken.

C.

Official statistics were collected at the time of the race.

D.

This information is not given.

Specify the categorical variables for this problem. Select all that apply.

A.

Winner

B.

Jockey

C.

Track Condition

D.

​Winner's payoff

E.

Duration

F.

Year

G.

Margin

H.

There are no categorical variables.

Specify the quantitative variables and identify the units for this problem. Select all that apply.

A.

​Year; the units are years

B.

​Winner's payoff; the units are dollars

C.

​Winner; the units not specified

D.

Track​ condition; the units not specified

E.

​Jockey; the units not specified

F.

​Duration; the units are minutes and seconds

G.

​Margin; the units are lenghts

H.

There are no quantitative variables.

Specify whether the data come from a designed survey or experiment. Choose the correct answer below.

A.

Experiment

B.

Designed survey

C.

This information cannot be determined by the given data.

Are the variables time series or​ cross-sectional?

Time series

​Cross-sectional

Neither

Specify any concerns. Select all that apply.

A.

The data sample size was too large.

B.

There are too many quantitative variables.

C.

The data collection was done incorrectly.

D.

There are no specific concerns.

Given the following numbers: 25 16 61 18 15 20 15 20 24 17 19 28, derive the mean, median, mode, variance, standard deviation, skewness, kurtosis, range, minimum, maximum, sum, and count. Interpret your results. What is the empirical rule for two standard deviations of the data?

The lowest and highest observations in a population are 14 and 48, respectively. What is the minimum sample size n required to estimate μ with 90% confidence if the desired margin of error is E = 1.5? What happens to n if you decide to estimate μ with 95% confidence? (You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places and "z" value to 3 decimal places. Round up your answers to the nearest whole number.)

John is lying on the sidewalk after robbing a bank, in pain and mulling over how to quantify the uncertainty of his survival, when Dirty Harry walks over. Dirty Harry pulls out his 44 Magnum and puts two bullets opposite each other in the six slots in the cylinder (e.g., if you number them 1 .. 6 clockwise, he puts them in 1 and 4), spins the cylinder randomly, and, saying "The question is, are you feeling lucky, probabalistically speaking, computer science punk?" points it at John head and pulls the trigger.... "CLICK!" goes the gun (no bullet) and Dirty Harry smiles... "How about that .... Let's see if this gun is memory-less!" Without spinning the cylinder again, he points the gun at Wayne's head and pulls the trigger again.

(a) What is the probability that (at least in my dream) John is hit?

(b) Now, suppose that when Dirty Harry put the bullets in the gun, he put them right next to each other (e.g., in slots 1 and 2). He spins it as usual. What is the probability in this case John is hit?

(c) Suppose Dirty Harry puts the bullets in two random positions in the cylinder and we don't have any idea where they are. He spins it as usual. Now what is the probability that John will be hit?