Consider the following regression output with Sunday circulation of newspapers as dependent variable and Daily circulation as independent variable. Both Sunday and Daily circulation and measured in thousands of copies.

Dependent Variable: Sunday
Variable:	Intercept	Daily
Coefficient	24.763	1.351
Std. Error	46.99	0.09
t Stat	0.527	14.532
P-value	0.602	0.000

Given the output above choose whether the following statement is TRUE or FALSE.

Question 1
This regression is bad because we are only 39.8% confident that the intercept coefficient is not 0.

a: TRUE

b: FALSE Question 2 ( it part 2 of the first queestion) Consider again the regression output of Question 1. How much confidence do you have that Daily increase of two thousand copies will result in Sunday increase of at least 2340 copies? a: less than 50% confidence b: at least 95% confidence but less than 99.7% confidence c: at least 99.7% confidence d: I do not have enough information to determine the confidence.

1. Quinnipiac University conducted a telephone survey with a randomly selected national sample of 1155 registered voters. The survey asked the respondents, “In general, how satisfied are you with the way things are going in the nation today?” (Quinnipiac University, February 7, 2017). Response categories were Very satisfied, Somewhat satisfied, Somewhat dissatisfied, Very dissatisfied, Unsure/No answer. a. What is the relevant population? b. What is the variable of interest? Is it qualitative or quantitative? c. What is the sample and sample size? d. What is the inference of interest to Gallup; that is, what are they trying to measure or learn about? e. What method of data collection is employed? f. How likely is the sample to be representative? g. Would it make more sense to use averages or percentages as a summary of the data for this question? h. Of the respondents, 24% said they felt somewhat satisfied. How many individuals provided this response?

find the sample size needed to give a margin of error to estimate a proportion within plus minus 2% within 99% confidence within 95% confidence within 90% confidence assume no prior knowledge about the population proportion p

Use R to complete the following questions. You should include your R code, output and plots in your answer.

1. Two methods of generating a standard normal random variable are:

a. Take the sum of 5 uniform (0,1) random numbers and scale to have mean 0 and standard deviation 1. (Use the properties of the uniform distribution to determine the required transformation).

b. Generate a standard uniform and then apply inverse cdf function to obtain a normal random variate (Hint: use qnorm).

For each method generate 10,000 random numbers and check the distribution using

a. Normal probability plot

b. Mean and standard deviation

c. The proportion of the data lying within the theoretical 2.5 and 97.5 percentiles and the 0.5 and 99.5 percentiles. (Hint: The ifelse function will be useful)  

These problems may be solved using Minitab. Copy and paste the appropriate Minitab output into a word-processed file. Add your explanations of the output near the Minitab output. DO NOT SIMPLY ATTACH PAGES OF OUTPUT AS AN APPENDIX.

Each problem should be able to fit on one or two pages, and each problem should include the following:

• Minitab output for the ANOVA.
• Written statement interpreting the ANOVA.
• Four-in-one plot of the residuals.
• Written interpretation as to whether the three assumptions of the ANOVA were met.
• Tukey comparisons if necessary.
• A written summary of your interpretation of the analysis in terms of the problem. This may involve more than one statement. In other words, state which group is “best” in terms of the problem.

1. Battery life for competing smartphone designs are being studied. 5 models of phone were fully charged and set to play the same video on repeat (the volume and brightness levels were to the same levels using laboratory instruments). The test was replicated 10 times for each phone, with the time until the phone turned off recorded (in hours). Analyze this problem as a CRD ANOVA to determine if the phone models differ in their battery life, and how they differ. If they are necessary, perform Tukey comparisons using Minitab AND BY HAND.

Design 1	Design 2	Design 3	Design 4	Design 5
12.2	12.2	10.0	10.2	11.0
12.4	13.4	11.2	7.9	12.5
11.9	12.4	8.9	9.1	11.7
11.7	11.0	11.2	11.2	10.8
11.7	12.4	10.2	10.1	10.0
12.0	13.1	10.6	6.6	9.8
11.8	11.5	10.4	8.1	10.3
11.5	11.6	9.2	10.0	9.3
13.9	13.3	10.8	8.7	11.1
13.2	12.7	11.5	8.4	12.9

2. Lactation promotes a temporary loss of bone mass to provide adequate

amounts of calcium for milk production. Consider the data on total

body bone mineral content for a sample both during lactation (L) and

in the post weaning period (P).

1 . 2    3 4 5    6    7 8    9    10

L 1928 2549 2825 1924 1628 2175 2114 2621 1843 2541

P 2126 2885 2895 1942 1750 2184 2164 2626 2006 2627

Does the data suggest that true average total body bone mineral con-

tent during post weaning exceeds that during lactation by more than

25g? Use results from an output you obtained from the R software to

state and test the appropriate hypotheses with 95% confidence level(show

all details of R, either print our the R code and result or hand-write

R code and result ). State any assumptions required for the test to be

valid.

5. The following table summarizes the skin colours and position of 368

NBA players in 2014. Suppose that an NBA player is randomly selected

from that years player pool.

2

Guard positionForward Center Total

white 26 30    28 84

skin colour black 128 122    34    284

Total 154 152    62    368

(a) Find out where the variable "skin colour" is independent with the

variable "position" with

alpha = 0.05

(b) We only concern about the variable "position". The media claims

that the proportion of "Guard" is the same as the proportion of "For-

ward", which is twice as the proportion of "Center". Conduct a test to

find out whether the statement is valid with 90% confidence interval.

(hint: to test H0: P1= 0.4, P2 = 0.4, P3= 0.2)

6. Complete the following ANOVA table ( find the value of ?1, ?2, ?3, ?4,

?5) [5] and give the null hypothesis and the alternative hypothesis, [2]

give your conclusion based on the ANOVA table [2].

ANOVA table

Df SumSq Mean Sq F value P value

brands 3 39.757 ?1 ?5 5.399e-07

Error    36 ?2 ?3

Total    ?4 . 68.128

7. Refer to the

Bulletin of Marine Science (April 2010)

study of teams

of shermen shing for the red apiny lobster in Baja Valifornia Sur,

Mexico. Two variables measured for each of 8 teams from the Punta

Abreojos shing cooperative were y=total catch of lobsters (in kilo-

grams) during the season and x=average percentage of traps allocated

per day to exploring areas of unknown catch (called search frequency)

total catch search frequency

2785 35

6535 21

6695    26

4891    29

4937    23

5727    17

7019 21

5735 20

(a) Graph the data in a scatterplot (using R). What type of trend, if any,

could be observed?

(b) Add the regression line to the plot (using R, either hand-write the R

code and plot the graph or print your R code and graph).

(c)Give the null and alternative hypothesis for testing whether total catch

is negatively linearly related to search frequency. Find the p-vale of the test

and give the appropriate conclusion of the test using alpha = 0.05

(d) what's the coefficient of correlation between total catch and search

frequency?

What are the advantage and disadvantage of assuming quadratic utility functions in mean variance analysis?

Construct a scatter plot. Find the equation of the regression line. Predict the value of y for each of the x-values. Use this resource: Regression Give an example of two variables that have a positive linear correlation.

Give an example of two variables that have a negative linear correlation.

Give an example of two variables that have no correlation.

Height and Weight: The height (in inches) and weights (in pounds) of eleven football players are shown in this table.

Height, x 62 63 66 68 70 72 73 74 74 75 75 Weight, y 195 190 250 220 250 255 260 275 280 295 300

x = 65 inches x = 69 inches x = 71 inches

A random sample of 130 observations produced a mean of ?⎯⎯⎯=36.1x¯=36.1 from a population with a normal distribution and a standard deviation σ=4.87.

(a) Find a 95% confidence interval for μ
≤ μ ≤

(b) Find a 99% confidence interval for μ
≤ μ ≤

(c) Find a 90% confidence interval for μ
≤ μ ≤

Given are five observations for two variables, x and y. x i 1 2 3 4 5 y i 4 7 6 11 13 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 3. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 3. to c. Using the following equation: Estimate the standard deviation of an individual value of y when x = 3. d. Using the following expression: Develop a 95% prediction interval for y when x = 3. If your answer is negative, enter minus (-) sign. to

The average number of words in a romance novel is 64,290 and the standard deviation is 17,422. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(___,____)

b. Find the proportion of all novels that are between 57,321 and 71,259 words. _____

c. The 95th percentile for novels is ____ words. (Round to the nearest word)

d. The middle 50% of romance novels have from ____words to_____ words. (Round to the nearest word)

find the sample size needed to give with 99% confidence a margin of error of plus or minus 5% when estimating proportion within plus minus 4% within plus minus 1%

The mean output of a certain type of amplifier is 496 watts with a variance of 144. If 40 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 1.2 watts? Round your answer to four decimal places.

The College Board wanted to test whether students graduating from private colleges and students graduating from public universities had different amounts of student loan debt. A sample of students from 146 private colleges across the country yielded an average loan debt of $29,972 with a standard deviation of $3,200. A sample of students from 225 public universities yielded an average loan debt of $28,762 with a standard deviation of $5,600. Conduct the test at the α=0.02α=0.02 level of significance.

What is meant by an absolute effect in epidemiologic research? Present at least one relevant example.