Construct the probability distribution for the value of a 2-card hand dealt from a standard deck of 52 cards (all face cards have a value of 10 and an ace has a value of 11).

1. what is the probability of being dealt 21?
2. what is the probability of being dealt 16?

3. construct a chart for the cumulative distribution function. what is the probability of being dealt a 16 or less? Between 12 and 16? between 17 and 20?

4. find the expected value and standard deviation of a 2-card hand.

Suppose that a market research analyst for a cell phone company conducts a study of their customers who exceed the time allowance included on their basic cell phone contract; the analyst finds that for those people who exceed the time included in their basic contract, the excess time used follows an exponential distribution with a mean of 22 minutes. Consider a random sample of 144 customers who exceed the time allowance included in their basic cell phone contract.

a. Find P(20 < x¯ < 30).

b. Find P(Σx is at least 3,000).

c. Find the 75th percentile for the sample mean excess time of 144 customers.

d. Find the 85th percentile for the sum of 144 excess times used by customers.

1.)The ages of millionaires in a city are normally distributed with a population standard deviation of 3 years and an unknown population mean. A random sample of 23 millionaires is taken and results in a sample mean of 44 years.

Find the margin of error for a 95% confidence interval for the population mean.

You may use a calculator or the common z values above.

• Round the final answer to two decimal places.

2.) A college admissions director wishes to estimate the mean age of all students currently enrolled. The age of a random sample of 23 students is given below. Assume the ages are approximately normally distributed. Use Excel to construct a 90% confidence interval for the population mean age. Round your answers to two decimal places and use increasing order

Age
25.8
22.2
22.5
22.8
24.6
24.0
22.6
23.6
22.8
23.1
21.5
21.4
22.5
24.5
21.5
22.5
20.5
23.0
25.1
25.2
23.8
21.8
24.1

Please answer a statistic problem(please answer all subquestions). Thank you very much.

NCbirths, cont' d. This time we will use a subset of the dataset after removing premature birth (36 weeks or sooner) and continue to use MomRace as the explanatory variable to predict birth weight.

To get NCbirths:

install.packages("Stat2Data")
library(Stat2Data)
data("NCbirths")

(a) Use the following R command to remove premature birth and create a dataset noPremie.

noPremies<-subset(NCbirths, NCbirths$Premie==0) ##subset(dataName, condition)

(b) Construct a side-by-side boxplot of birth weights separated by MomRate.

(c) Use tapply() or mean() to estimate group effects (αk)

(d) Conduct ANOVA F-test to assess whether there is at least one group effect statistically significant.

i) Copy and paste ANOVA table generated using R,

ii) check assumptions,

iii) Write all the 5 steps of the hypothesis test.

(e) Modify R command provide below to apply Fisher’s LSD to investigate which racial groups differ significantly from which others. Copy and paste R output. Summarize your conclusion.

#install.packages("agricolae")

#install outside r markdown, install in the Rstudio console or in an R script.

library(agricolae)

LSD.test(yourANOVAmodel, "groupVariableName", group=FALSE, console=T)

(f) This is a fairly large sample (over 1200 observations after removing premature births) so even relatively small difference in group means might yeild significant results. Do you think that the difference in mean birth weight among these racial groups are important in a practical sense? (Hint: do you think the estimated group effect (αk) from part (c) are meaningful in reality?) Explain briefly.

13.28 800 on the SAT. It is possible to score higher than 800 on the SAT, but scores above 800 are reported as 800. (That is, a student can get a reported score of 800 without a perfect paper.) In 2014, the scores of college-bound senior men on the SAT Math test followed a Normal distribution with mean 530 and standard deviation 123. What percentage of scores were above 800 (and so reported as 800)?

Given the likelihood of θ with respect to sample D p(D|θ) = Q j p(xj |θ), where D = {x1, · · · , xn} is identically and independently distributed (i.i.d) sample points. Briefly describe how you would find the maximum likelihood estimation and the Bayesian estimation of θ.

Project: Assess the impact of teaching style (F2F, Web, Mixed) on mean introductory sociology grades. Please determine if any of the groups differentiate themselves from the others using the .05 probability level.

F2F Web Mixed

Person 1 94 80 85

Person 2 78 74 83

Person 3 87 75 79

Person 4 90 76 80

Person 5 82 83 80

Please determine if the groups differ significantly and what that means.

What is the difference between reporting an estimate of mu using a margin of error versus using a confidence interval?

A racing car consumes a mean of 99 gallons of gas per race with a standard deviation of 3 gallons.

If 37 racing cars are randomly selected, what is the probability that the sample mean would be greater than 100.2 gallons? Round your answer to four decimal places.

When we do find a significant ANOVA, we do not know where the difference lies. It could be that only two groups are significantly different, or that all three groups are significantly different. In your response you mention that one problem with t-tests is that they only compare two groups at a time. This creates another problem with conducting multiple t-tests, which is that it increases our chances of committing a type I error. In what way do post-hoc tests attempt to reduce this problem with conducting multiple t-tests?

(No scribbling/chicken scratch! Please show work)

1. A researcher at the Annenberg School of Communication is interested in studying the use of smartphones among young adults. She wants to know the average amount of time that college students in the United States hold a smartphone in their hand each day. The researcher obtains data for one day from a random sample of 25 college students (who own smartphones). She installs an app that registers whenever the smartphone is being held and the screen is on. The sample mean is 230 minutes, with a standard deviation of 11 minutes.

a) What is the 95% confidence interval for average daily time a smartphone is used among college students?

b) What value of t is used in the confidence interval?

c) What is the standard error?

d) What is the lower bound of the confidence interval and the upper bound of the confidence interval?

How to find the sample autocorrelation function (ACF) using SPSS and how to tell if the data show any stationarity

Amy and Lester are the owners of The Hardware Store on main street in a large town. Without consulting Amy, Lester hires an accountant to prepare a formal Balance Sheet, Income Statement, and Statement of Cash Flows for The Hardware Store. Amy understands the importance of having a Balance Sheet and Income Statement, but she does not understand the importance of having a Statement of Cash Flows. Amy reasons that examining the Cash account in the General Ledger is sufficient to know where the cash came from and where it was spent. Presume you are the accountant that was hired by Lester. It is your task to explain to Amy the purpose of the Statement of Cash Flows along with its uses and limitations. Please make your initial post your response to Amy.

The Grocery Manufactures of America reported that 76% of consumers read the ingredients listed on a product's label. Assume the a sample of 400 consumers is selected from the population.

a. Calculate the standard error of the proportion.

b. What is the probability that the sample proportion will be more than 81% of the population proportion?

c. What is the probability that the sample proportion will be within ± .03 of the population proportion?

d. Answer part (c) for a sample of 750 consumers.