4.170 Change in Stock Prices. Standard & Poor's maintains one of the most widely followed indices of large-cap American stocks: the S&P 500. The index includes stocks of 500 companies in industries in the US economy. A random sample of 50 of these companies was selected, and the change in the price of the stock (in dollars) over the 5-day period from August 2 to 6, 2010 was recorded for each company in the sample. The data are available in StockChanges.

a. Use StatKey to calculate a 95% confidence interval for the mean change in all S&P stock prices over these dates using the bootstrap percentiles method. Include a screen shot of your Statkey output with your homework submission, and write the confidence interval below.

b. Use only the confidence interval you created (do not find a p-value) to predict the results of a hypothesis test to see if the mean change for all S&P 500 stocks over this period is different from zero.

i. Define the parameter.

ii. State the hypotheses.

iii. What significance level are you able to use based on the confidence interval?

iv. State the conclusion using nontechnical language.

c. If any error were to occur in the decision to reject or fail to reject, would it be a Type I error or a Type II error?

d. Explain what an error of this type would mean in context.

SPChange
0.29
-0.06
0.34
0.7
0.42
0.22
0.12
0.03
-0.5
0.36
0.03
0.09
-0.12
0.03
-0.47
-3.27
0.35
-0.06
0.01
0.6
0.12
4.86
-0.77
-0.03
0.39
0.1
-0.12
0.47
-0.05
0.06
-0.03
0.15
0.31
-0.15
0.32
-2.66
0.22
-0.03
0.09
0.29
0.16
0.38
0.1
0.21
0.09
0.33
0.18
1.93
0.14
0.03

. TRUE/FALSE: (Please use one sentence to explain why it is FALSE if you decide that one statement is FALSE)

(a) The regression through origin model is designed to fit count responses only

(b) The Bonferroni method is always the best way of computing joint CI's of the mean responses, i.e., provides the group of CIs with the narrowest ranges which achieves the claimed family confidence coefficient.

(c) When you want to obtain the smallest variance of the "regression coefficient estimate", you might choose to control the response variable values.

(d) We do not have to check the model assumptions when the regression through origin model is used.

* You wanted to estimate the mean number of vehicles crossing a busy bridge in your neighborhood each morning during rush hour for the past year. To accomplish this, you stationed yourself and a few assistants at one end of the bridge on 31 randomly selected mornings during the year and counted the number of vehicles crossing the bridge in a 10-minute period during rush hour. You found the mean to be 119 vehicles per minute, with a standard deviation of 31.

(a) Construct the 95% confidence interval for the population mean (vehicles per minute).

.................. - .......................

(b) Construct the 99% confidence interval for the population mean (vehicles per minute)

..................... - .....................

* A college counselor wants to determine the average amount of time first-year students spend studying. He randomly samples 31 students from the freshman class and asks them how many hours a week they study. The mean of the resulting scores is 17 hours, and the standard deviation is 5.8 hours.

(a) Construct the 95% confidence interval for the population mean.
................— ...............

(b) Construct the 99% confidence interval for the population mean.

....................... - ....................

*A cognitive psychologist believes that a particular drug improves short-term memory. The drug is safe, with no side effects. An experiment is conducted in which 8 randomly selected subjects are given the drug and then given a short time to memorize a list of 10 words. The subjects are then tested for retention 15 minutes after the memorization period. The number of words correctly recalled by each subject is as follows: 6, 11, 12, 4, 6, 7, 8, 6. Over the past few years, the psychologist has collected a lot of data using this task with similar subjects. Although he has lost the original data, he remembers that the mean was 4.9 words correctly recalled and that the data were normally distributed.

(a) On the basis of these data, what can we conclude about the effect of the drug on short-term memory? Use α = 0.05_{2 tail} in making your decision.

t_crit = ±

As part of a study on transportation safety, the U.S. Department of Transportation collected data on the number of fatal accidents per 1000 licenses and the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Data collected over a one-year period follow. These data are contained in the file named “Safety.csv”.

1- Find the sample mean and standard deviation for each variable. Round your answers to the nearest thousandth.

2- Use the function lm() in R to run a simple linear regression model on the data provided. Use the function summary() in R to generate the regression output. Use the function aov() in R to generate the corresponding ANOVA table. You ought to be able to determine which is the dependent variable and which is the independent variable in this SLR model.

Please copy your R code and the result and paste them here.

3- Write down the estimated regression function below and provide a practical interpretation of the coefficient of the independent variable.

4- Please find a 95% confidence interval for the coefficient of the independent variable and provide a practical interpretation of this interval.

5- At the 5% level of significance, is there a significant relationship between the two variables? Why or why not?

6- What is the value of the coefficient of determination for this simple linear regression model? Provide a brief interpretation of this value.

7- Use the information from the ANOVA table to compute the standard error of estimate, a.k,a, residual standard error. This value must match the residual standard error in the regression summary.

8- What is the point estimate of the expected number of fatal accidents per 1000 licenses if there are 10% drivers under age in a city?

9- Suppose we want to develop a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21. What is the estimate of the standard deviation for this confidence interval?

10-Suppose we want to develop a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21. Compute the t value and the margin of error needed for this confidence interval.

Please copy your R code and the result and paste them here.

11-Provide a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21 and a practical interpretation to this confidence interval.

12- Suppose we want to develop a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21. What is the estimate of the standard deviation for this prediction interval?

13- Suppose we want to develop a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21. Compute the margin of error needed for this prediction interval.

14- Provide a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21 and a practical interpretation to this prediction interval.'

PS: I do appreciate your help but please do not simply copy and paste the irrelevant answer

Safety.csv

The distribution of the number of eggs laid by a certain species of hen during their breeding period has a mean of 36 eggs with a standard deviation of 18.3. Suppose a group of researchers randomly samples 47 hens of this species, counts the number of eggs laid during their breeding period, and records the sample mean. They repeat this 1,000 times, and build a distribution of sample means. A) What is this distribution called? B) Would you expect the shape of this distribution to be symmetric, right skewed, or left skewed? Explain your reasoning. Left skewed, because the population distribution is left skewed. Left skewed, because according to the central limit theorem this distribution is approximately normal. Left skewed, because the population standard deviation is smaller than the population mean. Symmetric, because the population distribution is symmetric. Symmetric, because according to the central limit theorem this distribution is approximately normal. Symmetric, because the population standard deviation is smaller than the population mean. Right skewed, because the population distribution is right skewed. Right skewed, because according to the central limit theorem this distribution is approximately normal. Right skewed, because the population standard deviation is smaller than the population mean. C) Calculate the standard deviation of this distribution (i.e. the standard error). D) Suppose the researchers' budget is reduced and they are only able to collect random samples of 10 hens. The sample mean of the number of eggs is recorded, and we repeat this 1,000 times, and build a new distribution of sample means. What would be the standard error of this new distribution?

A study examined the average pay for men and women entering the workforce as doctors for 21 different positions.

(a) If each gender was equally paid, then we would expect about half of those positions to have men paid more than women and women would be paid more than men in the other half of positions. Write appropriate hypotheses to test this scenario.

(b) Men were, on average, paid more in 19 of those 21 positions. Complete a hypothesis test using your hypotheses from part (a).

As part of a study on transportation safety, the U.S. Department of Transportation collected data on the number of fatal accidents per 1000 licenses and the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Data collected over a one-year period follow. These data are contained in the file named “Safety.csv”.

1- Find the sample mean and standard deviation for each variable. Round your answers to the nearest thousandth.

2- Use the function lm() in R to run a simple linear regression model on the data provided. Use the function summary() in R to generate the regression output. Use the function aov() in R to generate the corresponding ANOVA table. You ought to be able to determine which is the dependent variable and which is the independent variable in this SLR model.

Please copy your R code and the result and paste them here.

3- Write down the estimated regression function below and provide a practical interpretation of the coefficient of the independent variable.

4- Please find a 95% confidence interval for the coefficient of the independent variable and provide a practical interpretation of this interval.

5- At the 5% level of significance, is there a significant relationship between the two variables? Why or why not?

6- What is the value of the coefficient of determination for this simple linear regression model? Provide a brief interpretation of this value.

7- Use the information from the ANOVA table to compute the standard error of estimate, a.k,a, residual standard error. This value must match the residual standard error in the regression summary.

8- What is the point estimate of the expected number of fatal accidents per 1000 licenses if there are 10% drivers under age in a city?

9- Suppose we want to develop a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21. What is the estimate of the standard deviation for this confidence interval?

10-Suppose we want to develop a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21. Compute the t value and the margin of error needed for this confidence interval.

Please copy your R code and the result and paste them here.

11-Provide a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21 and a practical interpretation to this confidence interval.

12- Suppose we want to develop a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21. What is the estimate of the standard deviation for this prediction interval?

13- Suppose we want to develop a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21. Compute the margin of error needed for this prediction interval.

14- Provide a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21 and a practical interpretation to this prediction interval.

Ps: I do appreciate your help But please do not simply copy and paste irrelevant answer, Thanks

One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. The store had the business objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. Data were collected from 40 complaints that were made in the past year (furniture2.xlsx). (a) The installation supervisor claims that the mean number of days between the receipt of a complaint and the resolution of the complaint is 30 days. To test the claim, build null and alternative hypotheses (for a two-tail test). (b) To conduct a two-tail t test based on the hypotheses in (a), identify the rejection regions (two sides) given the 99% critical level. (c) Using the given data, compute the test statistic for the t test. (d) At the 0.01 level of significance, should the claim be rejected (i.e., the mean number of days is different from 30)? In the critical-value approach, what is your conclusion based on (b) and (c)? Explain. (e) Using the test statistic in (c), determine the p-value for the t test. (f) In the p-value approach, what is your conclusion based on (e)? Explain.

what are the conditions and assumptions necessary to construct confidence interval on the mean and the variance separately?

Below is a list of the profit or (loss) of 40 companies.

- Calculate the population parameters for all 40 companies profit or loss

- Select a sample of 10

- Calculate the point estimators of the sample

- Compare the results (Point estimators with Population Parameters)

$ In Millions

$9,862             $19,710          

$44,940           $48,351

$10,558           $5,070

$6,662             $3,033

$29,450           ($3,864)

7,602               $364.5

$9,195             $1,288

$2,679             $30,101           

$1,907             ($5786)

$4,078             $24,441

$2,463             $12,662

$8,630             $18,232

$4,517.4          $22,183

$8,197             $5,106

$3,842.8          $21,204

$4,065             $22,714

$2,997             $9,609

$246.5             $4,286

$3,577             $2,736

$2,421.9          $1,982

Question 3 This question is testing your understanding of some important concepts about hypothesis testing and confidence intervals. For each part below, answer the question (1 mark) and then succinctly explain your reasoning (1 mark). (a) We are performing a one-sample t test at the 5% level of significance where the hypotheses are 0 1 H VH :5 :5 µ µ = ≠ . The number of observations is 15. State the critical value? (b) We are performing a hypothesis test and we conclude that we reject H0 at the 5% level of significance. Will we reject the same H0 (with the same H1 ) at the 10% level of significance? (c) Suppose we are performing a hypothesis test and we conclude that we cannot reject H0 at the 5% level of significance. Can we reject the same H0 (with the same H1 ) at the 10% level of significance? (d) Suppose we are performing a two-sample proportion test at the 5% level of significance where the hypotheses are 01 2 11 2 H p p VH p p : 0: 0 −= −≠ . The calculated p-value is 0.00268. Do we reject H0 ? (e) Based on the data, we obtain (1.85, 1.95) as the 95% confidence interval for the true mean. Can we reject 0 H : 0 µ = against 1 H : 0 µ ≠ at the 5% level of significance?

Problem 1.

(a) The columns of response and factors can be defined in R as follows, use these codes to solve the problem.

y<-c(2, 3, 10, 12, 8, 4, 11, 8)##response : scores

a<-c("Heart","Heart", "Soul", "Soul","Heart","Heart", "Soul", "Soul")##factor A

b<-c("D", "D", "D", "D", "R", "R", "R", "R")##factor B (group variable)

(b) Find the overall mean, row means, column means, each cell mean for the table given in problem 1.

A data set includes 103 body temperatures of healthy adult humans having a mean of 98.5°F and a standard deviation of 0.61°F. Construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body​ temperature?

What is the confidence interval estimate of the population mean μ​?

°F < μ < °F

​(Round to three decimal places as​ needed.)

When applying statistical tests involving comparing two means or a sample to a population mean, there are many organizational applications. For example, Human Resources may want to track entrance exam scores of their new hires. This would be an example of two mean comparison. In terms of the recent election, Gallup may take a sample and compare to a population of candidate votes (sample mean compared to a population mean).

Think of an example in your organization of either one of these tests and discuss its application as well as the risk of type 1 or 2 errors.