Nakamura et al. studied subjects with medial collateral ligament (MCL) and anterior cruciate ligament (ACL) tears. Between February 1995 and December 1997, 17 consecutive patients with combined acute ACL and grade III MCL injuries were treated by the same physician at the research center. One of the variables of interest was the length of time in days between the occurrence of the injury and the first magnetic resonance imaging (MRI). We wish to know if we can conclude that the mean number of days between injury and initial MRI is not 15 days in a population presumed to be represented by these sample data. Let ? = 0.05. 1. Set up the hypotheses. [2 points] 2. Draw a normal distribution graph with a critical value and shade the rejection region with proper size. [2 points] 3. Find the critical value from the table. [2 points]

The following are data on

y = quit rate per 100 employees in manufacturing

x = unemployment rate

The data are for United States and cover the period 1990-2002.

(a) Estimate the regression and report the results

(b) Construct a 95% confidence interval for β.

(c) Test the hypothesis H₀ : β = 0 against the alternative β=0 at the 5% significance level.

(d) Test Normality of the residuals using Jarque-Bera test.

(e) What is likely to be wrong with the assumptions of the classical normal linear model in this case? Discuss.

The table below shows the number of cars (in millions) sold in the United States for various years and the percent of those cars manufactured by GM. Year Cars Sold (millions) Percent GM Year Cars Sold (millions) Percent GM 1950 6.0 50.2 1985 15.4 40.1 1955 7.8 50.4 1990 13.5 36.0 1960 7.3 44.0 1995 15.5 31.7 1965 10.3 49.9 2000 17.4 28.6 1970 10.1 39.5 2005 16.9 26.9 1975 10.8 43.1 2010 11.6 19.1 1980 11.5 44.0 2015 17.5 17.6 Use a statistical software package to answer the following questions.

A. State the decision rule for 0.01 significance level: H0: ? ? 0; H1: ? < 0. REJECT H0 IF T < ?

B. Compute the value of the test statistic.

It appears that over the past 50 years, the number of farms in the United States declined while the average size of farms increased. The following data provided by the U.S. Department of Agriculture show five-year interval data for U.S. farms. Use these data to develop the equation of a regression line to predict the average size of a farm (y) by the number of farms (x). Discuss the slope and y-intercept of the model.

(Do not round the intermediate values. Round your answers to 2 decimal places.)

y^= ______ +( _____ )x

It appears that over the past 50 years, the number of farms in the United States declined while the average size of farms increased. The following data provided by the U.S. Department of Agriculture show five-year interval data for U.S. farms. Use these data to develop the equation of a regression line to predict the average size of a farm (y) by the number of farms (x). Discuss the slope and y-intercept of the model.

(Do not round the intermediate values. Round your answers to 2 decimal places.)

y^=   +(   )x

So far this year, U.S.-listed biotech companies have raised roughly $9.4 billion in initial public offerings, already beating the $6.5 billion raised in all of 2018, the biggest year on record, according to Dealogic data going back to 1995. This year’s biotech issues have jumped an average of 34% on their first day of trading, the biggest average first-day pop for the sector since the tech boom in 2000. The recent surge in biotech stocks extends beyond IPOs, as investors chase companies working on potential vaccines to combat Covid-19. They also anticipate the industry may benefit from more investment by governments in drug discovery and development.

A. Why are some market participants skeptical of investors' enthusiasm for biotech shares?

B. According to the article, what are the risks associated with investing in early-stage biotechnology companies?

Below are Global carbon dioxide concentrations and the measured change in Global temperature (Temperature Anomaly) for a period in our recent past:

Using StatCrunch, construct a scatterplot that shows the relationship between the two variables (carbon dioxide concentrations and the measured change in Global temperature). Calculate the r value using StatCrunch. Copy and Paste your work from StatCrunch into your Word document submission. Verbally describe the direction and magnitude of the relationship you find. What does this tell you about Global warming?

The following data set provides information on the lottery sales, proceeds, and prizes by year in Iowa.

FY

Sales

Proceeds

Prizes

1992

$166,311,122

$45,678,558

$92,939,035

1993

$207,192,724

$56,092,638

$116,820,274

1994

$206,941,796

$56,654,308

$116,502,450

1995

$207,648,303

$58,159,175

$112,563,375

1996

$190,004,182

$51,337,907

$102,820,278

1997

$173,655,030

$43,282,909

$96,897,120

1998

$173,876,206

$42,947,928

$96,374,445

1999

$184,065,581

$45,782,809

$101,981,094

2000

$178,205,366

$44,769,519

$98,392,253

2001

$174,943,317

$44,250,798

$96,712,105

2002

$181,305,805

$48,165,186

$99,996,233

HelpCopy to ClipboardDownload CSV

Create a graph using the sales and year. What approximate range of sales would you expect for the year 2017?

Select the correct answer below:

Between 250 and 300 million dollars

Between 300 and 375 million dollars

Between 375 and 400 million dollars

Between 500 and 550 million dollars

The following data set provides information on the lottery sales, proceeds, and prizes by year in Iowa.

FY

Sales

Proceeds

Prizes

1992

$166,311,122

$45,678,558

$92,939,035

1993

$207,192,724

$56,092,638

$116,820,274

1994

$206,941,796

$56,654,308

$116,502,450

1995

$207,648,303

$58,159,175

$112,563,375

1996

$190,004,182

$51,337,907

$102,820,278

1997

$173,655,030

$43,282,909

$96,897,120

1998

$173,876,206

$42,947,928

$96,374,445

1999

$184,065,581

$45,782,809

$101,981,094

2000

$178,205,366

$44,769,519

$98,392,253

2001

$174,943,317

$44,250,798

$96,712,105

2002

$181,305,805

$48,165,186

$99,996,233

HelpCopy to ClipboardDownload CSV

Create a graph using the sales and year. What approximate range of sales would you expect for the year 2017?

Select the correct answer below:

Between 250 and 300 million dollars

Between 300 and 375 million dollars

Between 375 and 400 million dollars

Between 500 and 550 million dollars

The Bureau of Economic Analysis in the U.S. Department of Commerce reported that the mean annual income for a resident of North Carolina is $18,688 (USA Today, August 24, 1995). A researcher for the state of South Carolina wants to see if the mean annual income for a resident of South Carolina is different. A sample of 400 residents of South Carolina shows a sample mean annual income of $16,860 and the population standard deviation is assumed to known,  =$14,624. Use a 0.05 level of significance, the researcher wants to test the following hypothesis.

H0:  = 18,688 Ha:   18,688

a) Use confidence interval approach to test the hypothesis?

b)What is your conclusion?

C)What are three rejection rules (You have used confidence interval approach in Question 2)?

D)Do three rejection rules lead to the same conclusion? What is your conclusion?