Suppose you were asked to investigate which predictors explain the number of minutes that 10- to18-year-old students spend on Twitter. To do so, you build a linear regression model with Twitter usage (Y) measured as the number of minutes per week. The four predictors you include in the model are Height, Weight, Grade Level, and Age of each student. You build four simple linear regression models with Y regressed separately on each predictor, and each predictor is statistically significant. Then you build a multiple linear regression model with Y regressed on all four predictors, but only one predictor, Age, is statistically significant, and the others are not. What is likely going on among the four predictors? If you include more than one of these predictors in the model, what are some problems that can result?

3. In the following situations, identify the random variable of interest (e.g. ”Let X be the number of ...”). Then state whether or not the r.v. is binomial, justifying your answer.

(a) A police officer randomly selects 30 cars to find out how many do not have

a current Warrant of Fitness (WOF). She knows from experience that the

probability a car does not have a current WOF is 1.6

(b) A data collector goes from house to house in a Wellington suburb to find the number of houses where the person answering the door (over the age of 18) agrees with a particular housing policy of the current government. The probability that a randomly selected adult in New Zealand agrees with the policy is known to be 0.4. The collector will stop collecting responses once they have 100 responses.

(c) Mike is repeatedly rolling two dice and will stop when he gets a double six. He counts the number of rolls until he gets a ’success’.

There is a wealth of information available on how companies can select projects which will be profitable, how to align projects with a company's strategic objectives, how to evaluate proposals, and in general, how to have a successful project.   Yet while projects today are more successful than ever, a substantial number still fail.

Consider some projects that you have worked on either at your job (e.g. office software upgrades, new accounting system, moving to a new location) or in your personal life (e.g. a wedding, modernizing a kitchen, an extensive vacation). Please try and explain why the project you worked on was successful or a failure.

TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streaming is gaining in popularity. A poll reported that 57% of 2342 American adults surveyed said they have watched digitally streamed TV programming on some type of device. (a) Calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time. (Round your answers to three decimal places.) , Interpret the resulting interval. We are 99% confident that this interval does not contain the true population proportion. We are 99% confident that this interval contains the true population proportion. We are 99% confident that the true population proportion lies below this interval. We are 99% confident that the true population proportion lies above this interval. Correct: Your answer is correct. (b) What sample size would be required for the width of a 99% CI to be at most 0.04 irrespective of the value of p̂? (Round your answer up to the nearest integer.)

1. According to the American Mathematical Society’s survey of recently-graduated PhD’s in Mathematics, 47% were white, 42% were Asian, 4% were Hispanic or Latino, 3% were Black or African American, and 4% were another race. Among job applicants for an entry-level math professorship, 101 were white, 87 were Asian, 6 were Hispanic or Latino, 4 were Black or African American, and 2 were another race. Is there a significant difference between the racial diversity of the applicants versus the racial diversity of recent math PhD graduates, at α = 0.05? Show all calculations by hand.

Suppose you have a theory that your organization's back safety training program is not producing notable results in reducing back injuries.  Your theory is that performing more back safety training is not corresponding to reduction in back injuries. You calculate the correlation coefficient comparing the number of back safety training sessions over the course of three years with the number of  back injuries. Your calculation yields the following number: 0.2. How would you, in statistical terms, describe the correlation number and what would you conclude regarding theory?

part1. A double-blind design is important in an experiment because there is a natural tendency for subjects in an experiment to want to please the researcher.

a. True

b. False

part 2.

Sampling error concerns natural variation between samples, and is always present.

a. True

b. False

part 3. Sampling error can only be eliminated when conducting a questionnaire of students and every question is a closed question.

a. True

b. False

The American Bankers Association reported that, in a sample of 125 consumer purchases in France, 63 were made with cash, compared with 26 in a sample of 50 consumer purchases in the United States.

Construct a 95 percent confidence interval for the difference in proportions. (Round your intermediate value and final answers to 4 decimal places.)

The 95 percent confidence interval is from ______ to _______ .

2) Natural History magazine has published a listing of the maximum speeds, in mph, for a wide variety of animals. A random sample of four of these animals, along with their maximum speeds, is shown below: Cheetah 70 mph Domestic Cat 30 mph Giraffe 32 mph Elephant 25 mph a) Compute the sample mean maximum speed of this sample of size 4. Show units. Do not approximate. b) The true mean maximum speed for all of the animals in this study is 30 mph. (  = 30 mph) Assuming there have been no mistakes in collecting, recording, or computing, find the sampling error. Show units.

A company is experimenting with synthetic fibers as a substitute for natural fibers.

The quality characteristic of interest is the breaking strength. A random sample of 8 natural fibers yields an average breaking strength of 540 kg with a standard deviation of 55 kg. A random sample of 10 synthetic fibers gives a mean breaking strength of 610 kg with a standard deviation of 22 kg.

(a) Can you conclude that the variances of the breaking strengths of natural and synthetic fibers are different? Use a level of significance α of 0.05.

(b) Find a two-sided 95% confidence interval for the ratio of the variances of the breaking strengths of natural and synthetic fibers.

You may need to use the appropriate appendix table or technology to answer this question.
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.
(a)
State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let p1 = population proportion most recently saying financial security more than fair and p2 = population proportion from the year before saying financial security more than fair. Enter != for ≠ as needed.)
H0:  

Ha:  

(b)
Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
Find the value of the test statistic. (Use
p1 − p2.
Round your answer to two decimal places.)
  

Find the p-value. (Round your answer to four decimal places.)
p-value =   
Incorrect:
State your conclusion.
Do not reject H0. There is insufficient evidence to conclude the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.
Do not reject H0. There is sufficient evidence to conclude the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.   
Reject H0. There is insufficient evidence to conclude the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.
Reject H0. There is sufficient evidence to conclude the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.
Correct: Your answer is correct.
(c)
What is the 95% confidence interval estimate of the difference between the two population proportions? (Round your answers to four decimal places.)
  
_____
to   
_____
What is your conclusion?
The 95% confidence interval zero, so we can be 95% confident that the population proportion of adults saying that their financial security is more than fair .

The data below are for 30 people. The independent variable is “age” and the dependent variable is “systolic blood pressure.” Also, note that the variables are presented in the form of vectors that can be used in R.

age=c(39,47,45,47,65,46,67,42,67,56,64,56,59,34,42,48,45,17,20,19,36,50,39,21,44,53,63,29,25,69)

systolic.BP=c(144,20,138,145,162,142,170,124,158,154,162,150,140,110,128,130,135,114,116,124,136,142,120,120,160,158,144,130,125,175)

1. Using R, develop and show a scatterplot of systolic blood pressure (dependent variable) by age (independent variable), and calculate the correlation between these two variables.
2. Assume that these data are “straight enough” to model using a linear regression line. Develop and show that model (write out the model in the terms of the problem), and also show in a plot the line that best fits these data.
3. Plot the residuals and comment on what you see as to how appropriate the model is.
4. Using a boxplot, determine if there are any outliers in systolic blood pressure. If so, point out which points are outliers, if any.
5. Assuming there is at least one outlier in systolic blood pressure, remove that outlier and re-do parts a) through c) again using the remaining data without the outlier(s). State and comment on this second model.
6. In your second model, explain in the context of age and systolic blood pressure what the slope of your fitted line means. Also, for your second model, calculate R² (the coefficient of determination), and explain what that means in the context of your second model.

Consider the following hypothesis test:

H ₀:   20

H _a:  < 20

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 3 decimals)?

c. Using  = .05, can it be concluded that the population mean is less than 20?

d. Using  = .05, what is the critical value for the test statistic?

e. State the rejection rule: Reject H ₀ if z is

greater than or equal to

greater than

less than or equal to

less than equal to

not equal toItem 5  the critical value.

A new roller coaster at an amusement park requires individuals to be at least​ 4' 8"

​(56 inches) tall to ride. It is estimated that the heights of​ 10-year-old boys are normally distributed with

mu equals μ=55.0 inches and sigma equals σ=4 inches.

a. What proportion of​ 10-year-old boys is tall enough to ride the​ coaster?

b. A smaller coaster has a height requirement of

50 inches to ride. What proportion of​ 10-year-old boys is tall enough to ride this​ coaster?

c. What proportion of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a?