Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.1 grams and a standard deviation of 2.2 grams. a) For samples of size 12 pizza slices, what is the standard deviation for the sampling distribution of the sample mean? State answer to five decimal places. b) What is the probability of finding a random slice of pizza with a mass of less than 66.5 grams? State the answer to four decimal places. c) What is the probability of finding a 12 random slices of pizza with a mean mass of less than 66.5 grams? State the answer to four decimal places. d) What sample mean (for a sample of size 12) would represent the bottom 15% (the 15th percentile)? State answer to one decimal place. grams

A study conducted by Stanford researchers asked children in two elementary schools in San Jose, CA to keep track of how much television they watch per week. The sample consisted of 198 children. The mean time spent watching television per week in the sample was 15.41 hours with a standard deviation of 14.16 hours.

(a) Carry out a one-sample t-test to determine whether there is convincing evidence that average amount of television watching per week among San Jose elementary children exceeds fourteen hours per week. (Report the hypotheses, test statistic, p-value, and conclusion at the 0.10 level of significance.)

(b) Calculate and interpret a one-sample 90% t-confidence interval for the population mean.

(c) Comment on whether the technical conditions for the t-procedures are satisfied here. [Hint: What can you say based on the summary statistics provided about the likely shape of the population?]

2.In a test of the hypothesis H0: μ = 50 versus Ha: μ < 50, a sample of 40 observations is selected from a normal population and has a mean of 49.0 and a standard deviation of 4.1.

a) Find the P-value for this test.

b) Give all values of the level of significance α for which you would reject H0.

3.In a test of the hypothesis H0: μ = 10 versus Ha: μ≠ 10, a sample of 16 observations possessed mean 11.4 and standard deviation 3.1.

a) Find the P-value for this test.

b) Give all values of the level of significance α for which you would not reject H0.

What is a linear regression analysis? What does it provide you? Your answer should address development of a linear response equation and associated uncertainty in prediction.

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a)

• Suppose n = 36 and
• p = 0.39.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo    

second blank

cancannot    

third blank

both n·p and n·q exceedn·p exceeds    n·p and n·q do not exceedn·q does not exceedn·p does not exceedn·q exceeds

fourth blank (Enter an exact number.)


What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ = mu sub p hat =

σ_p̂ = sigma sub p hat =

(b)

Suppose

• n = 25 and
• p = 0.15.

Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo    

second blank

cancannot    

third blank

both n·p and n·q exceedn·p exceeds    n·p and n·q do not exceedn·q does not exceedn·p does not exceedn·q exceeds

fourth blank (Enter an exact number.)

(c)

Suppose

• n = 46 and
• p = 0.33.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo    

second blank

cancannot    

third blank

both n·p and n·q exceedn·p exceeds    n·p and n·q do not exceedn·q does not exceedn·p does not exceedn·q exceeds

fourth blank (Enter an exact number.)


What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ = mu sub p hat =

σ_p̂ = sigma sub p hat =

The data set airquality is one of R’s included data sets. It shows daily measurements of ozone concentration (Ozone), solar radiation (Solar.R), wind speed (Wind), and temperature (Temp) for 5 summer months in 1977 in New York City. Some of the observations are missing and are recorded as NA, meaning not available. View an overall summary of the variables in airquality with the command

> summary(airquality) Ignore the summaries for Month and Day since those variables should be factors, not numeric variables, and their summaries are meaningless. Attach airquality to your workspace

> attach(airquality) and make boxplots of Ozone, Solar.R, Wind, and Temp. Comment on any noteworthy features.

Write a few sentences comparing bivariate correlation and bivariate regression. You need to discuss when it is appropriate to use each of these statistics.

Suppose Y is an random variable. If P(a<Y<2a)=0.16 and the median of Y is 5, what is a? Note: There may be more than one solution. Report all.

1. The Coefficient of Determination is *

a. the percent of variance in the dependent variable that can be explained by the independent variable

b. the ratio of the variance of Y to the variance of Y for a specific X

c. a measure of how strong the linear relationship is between the explanatory and response variables

2.

The null hypothesis for a regression model is state as *

a. beta_1=0: there is no relationship

b. beta_1 > 0: there is a positive relationship

c. rho=0: there is no relationship

d. rho < 1: there is a negative relationship

3.Choose the best interpretation of \beta_{0} *

a. the sample correlation between x and y

b. the change in y as x increases by 1 unit

c. the amount of uncertainty remaining after fitting the model

d. the value of y when all x's are zero

4.Linear regression analysis is used to assess the relationship between what two types of measurements? *

a. quantiative; quantitative

b. categorical; categorical

c. quantitative; categorical

1. Explain in words what a confidence interval means to someone who has never taken statistics.

2. There is concern that rural Minnesota is aging at a different rate than urban Minnesota. We want to test if the average age in rural Minnesota is different from the average age in urban Minnesota. Write out the null and alternative hypotheses.

3. At the 5% significance level, do you reject the null hypothesis? Why? Explain this to someone who has never taken statistics.

A random sample is drawn from a population with mean μ = 74 and standard deviation σ = 6.2. [You may find it useful to reference the z table.]

a. Is the sampling distribution of the sample mean with n = 18 and n = 47 normally distributed?

Yes, both the sample means will have a normal distribution.

No, both the sample means will not have a normal distribution.

No, only the sample mean with n = 18 will have a normal distribution.

No, only the sample mean with n = 47 will have a normal distribution.

b. Calculate the probability that the sample mean falls between 74 and 77 for n = 47. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

So this week we learned about the four V's of Big data - Velocity, Volume, Veracity and Variety. As we know the velocity of data can vary so does it affect the other three V's? How are they affected? Also same if there are changes in other or one of the V then how are the rest affected?

This assignment is a series of short answer, multiple choice, and fill-in-the-blank questions based on the article, “The Effects of Hospital-Level Factors on Patients' Ratings of Physician Communication” (Al-Amin & Makaremet, 2016).

What statistical techniques were used for the results presented in Table 2?  Summarize the findings from this statistical analysis (20 points).

Statistical Technique:

Findings based on statistical technique:

            Overall model:

            Individual factors:

Assume that z is the test statistic. (Give your answers correct to two decimal places.)

(a) Calculate the value of z for Ho: μ = 10, σ = 2.8, n = 36, x = 11.4.

_________

(b) Calculate the value of z for Ho: μ = 120, σ = 26, n = 26, x = 125.9.

_________

(c) Calculate the value of z for Ho: μ = 18.2, σ = 4.4, n = 140, x = 18.88.

__________

(d) Calculate the value of z for Ho: μ = 81, σ = 13.5, n = 52, x = 78.6.

___________

Conduct a hypothesis test to determine if  companies with negative revenue change tend to be on the (500) market less time (and/or how much less time)?

The data is below. Please show all work in excel.

Company Name	Revenue Change	# Years on Fortune 500 List
Walmart	3.00%	24
Exxon Mobil	17.40%	24
Berkshire Hathaway	8.30%	24
Apple	6.30%	24
UnitedHealth Group	8.80%	24
McKesson	3.10%	24
CVS Health	4.10%	24
Amazon.com	27.10%	17
AT&T	-2.00%	24
General Motors	-5.50%	24
Ford Motor	3.30%	24
AmerisourceBergen	4.30%	24
Chevron	25.10%	24
Cardinal Health	6.90%	24
Costco	8.70%	24
Verizon	0.00%	24
Kroger	6.40%	24
General Electric	-3.50%	24
Walgreens Boots Alliance	0.70%	24
JPMorgan Chase	8.00%	24
Fannie Mae	4.90%	21
Alphabet	22.80%	13
Home Depot	6.70%	24
Bank of America Corp.	7.00%	24
Express Scripts Holding	-0.20%	19
Wells Fargo	3.80%	24
Boeing	-1.20%	24
Phillips 66	26.50%	6
Anthem	6.10%	24
Microsoft	5.40%	24
Valero Energy	26.00%	20
Citigroup	6.80%	24
Comcast	5.10%	23
IBM	-1.00%	24
Dell Technologies	21.40%	21
State Farm Insurance Cos.	2.90%	24
Johnson & Johnson	6.30%	24
Freddie Mac	13.70%	21
Target	3.40%	24
Lowes	5.50%	24
Marathon Petroleum	21.00%	7
Procter & Gamble	-7.70%	24
MetLife	4.20%	24
UPS	8.20%	24
PepsiCo	1.20%	24
Intel	5.70%	24
DowDuPont	30.20%	24
Archer Daniels Midland	-2.40%	24
Aetna	-4.10%	18
FedEx	19.80%	24
United Technologies	4.50%	24
Prudential Financial	1.50%	24
Albertsons Cos.	1.60%	14
Sysco	9.90%	24
Disney	-0.90%	24
Humana	-1.10%	24
Pfizer	-0.50%	24
HP	7.90%	24
Lockheed Martin	0.80%	24
AIG	-5.40%	24
Centene	19.30%	9
Cisco Systems	-2.50%	22
HCA Healthcare	6.50%	24
Energy Transfer Equity	26.60%	12
Caterpillar	18.00%	24
Nationwide	9.60%	24
Morgan Stanley	15.00%	24
Liberty Mutual Insurance Group	11.40%	24
New York Life Insurance	3.70%	24
Goldman Sachs Group	12.00%	19
American Airlines Group	5.00%	24
Best Buy	7.00%	24
Cigna	4.90%	24
Charter Communications	43.40%	18
Delta Air Lines	4.00%	24
Facebook	47.10%	6
Honeywell International	3.10%	24
Merck	0.80%	24
Allstate	5.40%	23
Tyson Foods	3.70%	24
United Continental Holdings	3.20%	24
Oracle	1.80%	23
Tech Data	40.20%	24
TIAA	-2.90%	21
TJX	8.10%	24
American Express	5.20%	24
Coca-Cola	-15.40%	24
Publix Super Markets	1.60%	24
Nike	6.10%	24
Andeavor	42.50%	19
World Fuel Services	24.70%	14
Exelon	6.90%	24
Massachusetts Mutual Life Insurance	-11.40%	24
Rite Aid	6.90%	24
ConocoPhillips	33.80%	24
CHS	5.20%	19
3M	5.10%	24
Time Warner	6.70%	19
General Dynamics	-1.20%	24
USAA	10.60%	24