1) What are the 2 variables in a Regression Analysis and what are their levels of measurement?

2) What is the Chi-Square Goodness of Fit test and why would it be applied to a data set?

A. Determine the sample size required to estimate a population proportion to within 0.038 with 97.9% confidence, assuming that you have no knowledge of the approximate value of the sample proportion.

Sample Size =

B. Repeat part the previous problem, but now with the knowledge that the population proportion is approximately 0.29.

Sample Size =

A hotel chain wants to estimate the average number of rooms rented daily in each month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 24 rooms.
During January, a sample of 16 days has a sample mean of 48 rooms. This information is used to calculate an interval estimate for the population mean to be from 40 to 56 rooms. What is the level of confidence of this interval? Report the level of confidence as a percentage and use 2 decimal places.

You are constructing a 90% confidence interval for one population mean. A sample if size 20 is taken from the population of interest. The mean from the sample is 5 and the standard deviation is 1.5.

What is the t-score to be used in calculating Margin of Error? (do not round)

According to the 2010 US Census, the average number of residents per housing

unit for the n=87 counties in Minnesota was 2.10, and the standard deviation

was 0.38. Test whether the true mean number of residents per housing unit

in Minnesota in 2010 is less than the national value of 2.34 at the level

α

= 0

.

05.

a. Show all five steps of this test.

b. What type of error could we be making in this context?

c. What is the minimum average number of residents per household needed

in order to fail to reject H0? Assume the sample standard deviation is the same.

d. Suppose the true number of residents per household in Minnesota is normally

distributed with a mean of 2.0 and a standard deviation of 0.4. Suppose we reject

the null hypothesis if the sample means the number of residents is less than 2.27. What

is the probability of making a type II error?

Thanks for your speedy response!! Timed problem.

Data showing the values of several pitching statistics for a random sample of 20 pitchers from the American League of Major League Baseball is provided.

An estimated regression equation was developed to predict the average number of runs given up per inning pitched (R/IP) given the average number of strikeouts per inning pitched (SO/IP) and the average number of home runs per inning pitched (HR/IP).

(a)

Use the F test to determine the overall significance of the relationship.

State the null and alternative hypotheses.

H₀: β₁ = β₂ = 0
H_a: One or more of the parameters is not equal to zero.H₀: One or more of the parameters is not equal to zero.
H_a: β₁ = β₂ = 0    H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₁ = β₂ = 0
H_a: All the parameters are not equal to zero.H₀: β₀ = 0
H_a: β₀ ≠ 0

Calculate the test statistic. (Round your answer to two decimal places.)

Calculate the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion at the 0.05 level of significance?

Do not reject H₀. There is insufficient evidence to conclude that there is a significant overall relationship.Reject H₀. There is insufficient evidence to conclude that there is a significant overall relationship.    Do not reject H₀. There is sufficient evidence to conclude that there is a significant overall relationship.Reject H₀. There is sufficient evidence to conclude that there is a significant overall relationship.

(b)

Use the t test to determine the significance of SO/IP.

State the null and alternative hypotheses.

H₀: β₁ ≤ 0
H_a: β₁ > 0H₀: β₁ ≥ 0
H_a: β₁ < 0    H₀: β₁ = 0
H_a: β₁ > 0H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₁ = 0
H_a: β₁ ≠ 0

Find the value of the test statistic for β₁. (Round your answer to two decimal places.)

Find the p-value for β₁. (Round your answer to three decimal places.)

p-value =

What is your conclusion at the 0.05 level of significance?

Reject H₀. There is sufficient evidence to conclude that SO/IP is a significant factor.Do not reject H₀. There is sufficient evidence to conclude that SO/IP is a significant factor.    Do not reject H₀. There is insufficient evidence to conclude that SO/IP is a significant factor.Reject H₀. There is insufficient evidence to conclude that SO/IP is a significant factor.

Use the t test to determine the significance of HR/IP.

State the null and alternative hypotheses.

H₀: β₂ ≤ 0
H_a: β₂ > 0H₀: β₂ = 0
H_a: β₂ ≠ 0    H₀: β₂ ≠ 0
H_a: β₂ = 0H₀: β₂ ≥ 0
H_a: β₂ < 0H₀: β₂ = 0
H_a: β₂ > 0

Find the value of the test statistic for β₂. (Round your answer to two decimal places.)

Find the p-value for β₂. (Round your answer to three decimal places.)

p-value =

What is your conclusion at the 0.05 level of significance?

Reject H₀. There is insufficient evidence to conclude that HR/IP is a significant factor.Reject H₀. There is sufficient evidence to conclude that HR/IP is a significant factor.    Do not reject H₀. There is insufficient evidence to conclude that HR/IP is a significant factor.Do not reject H₀. There is sufficient evidence to conclude that HR/IP is a significant factor.

*Include all calculations and no excel please*

A buyer for National Sports must place orders with Saucony prior to the time the shows will be sold as they are manufactured overseas and shipping takes several months.  The buyer must decide on November 1 how many pairs of the latest model Saucony’s to order for sale during the coming summer season. Saucony’s ordering policy requires retailers to purchase shoes in lots of 100 pair.  Saucony charges National Sports $45 per pair.  National retails them at $70 per pair.  Any pairs remaining unsold at the end of the summer season will be sold at a 50% closeout sale next fall ($35 per pair).  Market research by Nielsen suggests the following probabilities of demand for the new shoes:

1. Draw and solve a decision tree for this problem. How many shoes should National order?  
2. How much profit will they actually earn?
3. Compute the value of perfect information regarding demand for the new style.
4. Ipsos is offering additional market research to help National refine the probability of demand.  The price of the market research is $5000.  Should you: (a) snatch it up because the price is below the value of perfect information, (b) draw and solve a value of sample information tree to determine how much the information is really worth in light of its accuracy since the price is below the value of perfect information, or (c) laugh in their face because the price is more than the value of perfect information and the offer is therefore overpriced.

The mean incubation time for a type of fertilized egg kept at a certain temperature is 17days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1day.

A. Find and interpret the probability that a randomly selected fertilized egg hatches in less than 16 days is? Round to 4 decimal places

B. Find and interpret the probability that a randomly selected fertilized egg takes over 18 days to hatch? Round to 4decimal places

C. Find and interpret that a randomly selected fertilized egg hatches between 15 and 17 days?

D. Would it unusual for an egg to hatch in less than 14 days . The probability of an egg hatching in less than 14 days is?

Problem 4: Teen smoking

According to a report published by the Centers for Disease Control and Prevention, about 20 percent of high school students currently use a tobacco product. This number of down from 23 percent in 2014. (https://www.cdc.gov/tobacco/data_statistics/fact_sheets/youth_data/tobacco_use/index.htm). We would like to conduct a study to evaluate high school students’ attitudes toward scenes of smoking in the movies. Suppose you randomly select students to survey them on their opinion about this question.

a) What is the probability that none of the first 4 students you interview is a smoker? (1 point)

b) What is the probability that there are no more than two smokers among 10 students you randomly choose? (2 points)

c) What is the probability that exactly 3 out of a new sample of 10 students do not smoke? (1 point)

data contained in the chart below (PGA Tour website, November 1, 2012) was used to develop an estimated regression equation to predict the average number of yards per drive given the ball speed and the launch angle.

Player Club Head Speed Ball Speed Launch Angle Total Distance

Bubba Watson 124.69 184.98 8.79 309.2

Dustin Johnson 121.62 180.57 11.30 301.8

J.B. Holmes 121.33 180.00 12.97 300.6

Rory McIlroy 120.21 178.07 11.25 298.6

Charlie Beljan 122.77 180.71 9.79 296.9

Robert Garrigus 121.39 180.21 12.31 296.5

John Daly 119.07 176.70 13.13 295.9

Gary Woodland 123.80 181.59 9.54 295.6

Adam Scott 119.30 176.81 9.29 295.3

Scott Piercy 117.59 174.42 11.64 295.0

Kyle Stanley 119.51 177.02 12.59 294.5

Keegan Bradley 116.83 172.35 12.61 294.3

Martin Laird 117.74 174.88 10.41 293.5

Ryan Palmer 116.12 172.43 13.31 293.2

Scott Stallings 118.85 175.48 10.74 293.1

Jason Day 119.16 176.87 11.88 292.7

Josh Teater 115.89 171.96 11.98 292.6

Harrison Frazar 114.39 169.80 12.32 292.1

Jhonattan Vegas 122.47 180.38 9.99 291.7

Louis Oosthuizen 116.79 173.32 10.59 291.3

Troy Matteson 116.55 172.48 13.09 291.1

Edward Loar 117.69 172.53 11.53 291.0

Sean O'Hair 116.52 172.87 11.84 290.7

Seung-Yul Noh 118.35 175.08 9.89 290.0

Graham DeLaet 120.04 176.71 11.86 289.7

Troy Kelly 115.64 171.38 9.97 289.7

Angel Cabrera 119.08 176.09 9.95 289.4

Lee Westwood 117.20 173.38 9.68 289.2

Jason Kokrak 118.14 175.31 10.72 288.9

Aaron Baddeley 119.05 176.75 9.04 288.7

Bill Haas 115.55 171.27 10.57 288.7

Martin Flores 118.93 175.38 9.73 288.6

Nick Watney 118.69 175.82 9.20 288.6

Phil Mickelson 116.81 173.18 10.35 288.5

Carl Pettersson 113.85 169.03 11.11 288.2

Harris English 117.43 174.16 10.03 288.2

Boo Weekley 114.87 170.52 9.41 287.9

Bo Van Pelt 114.09 169.38 11.91 287.8

Bobby Gates 119.63 175.51 9.03 287.8

Tiger Woods 120.94 177.69 10.67 287.8

Charles Howell III 118.16 173.88 8.45 287.5

Charley Hoffman 115.76 171.17 11.31 287.5

Vijay Singh 113.75 168.32 11.71 287.4

Rickie Fowler 115.64 171.41 11.72 287.3

Davis Love III 115.21 171.09 11.25 287.1

Erik Compton 114.56 170.04 12.06 287.1

Tommy Gainey 112.94 167.58 12.25 287.0

Daniel Chopra 116.88 172.20 11.74 286.8

John Rollins 113.54 168.34 11.53 286.7

Jeff Overton 112.04 166.07 11.65 286.6

Mark Anderson 117.84 174.76 9.58 286.4

Chris Couch 119.61 174.46 9.99 286.1

Jason Dufner 112.60 167.05 11.02 286.1

John Senden 115.90 171.66 9.80 286.0

Webb Simpson 113.34 166.74 10.47 285.8

Ernie Els 113.20 168.09 12.67 285.7

Kevin Chappell 117.22 172.05 10.88 285.7

Andres Romero 115.42 171.26 10.57 285.5

Charl Schwartzel 116.89 172.76 9.38 285.5

Robert Karlsson 116.86 173.67 10.85 285.5

Bud Cauley 112.39 166.45 13.32 285.4

Jonathan Byrd 115.14 170.67 10.47 285.4

Bill Lunde 111.97 166.16 10.97 285.3

Sergio Garcia 119.13 175.35 8.28 285.3

Greg Owen 118.85 174.38 9.11 285.2

Garth Mulroy 114.82 169.78 11.89 285.1

Steve Stricker 112.22 166.29 10.89 285.1

Hunter Mahan 112.05 166.15 11.12 284.8

Matt Jones 116.29 172.23 10.15 284.8

Rory Sabbatini 112.20 166.59 11.16 284.8

Scott Brown 112.53 165.95 11.90 284.8

Brian Harman 111.08 164.87 11.35 284.7

Jimmy Walker 117.43 174.04 9.93 284.7

Ryo Ishikawa 113.55 168.13 11.43 284.7

Billy Horschel 111.19 164.38 12.11 284.3

Chris Kirk 112.79 167.15 11.78 284.0

Camilo Villegas 113.03 167.86 11.31 283.9

Roberto Castro 112.82 166.77 10.73 283.8

John Merrick 113.11 167.87 9.87 283.7

Will Claxton 111.70 165.53 10.92 283.7

D.J. Trahan 114.75 169.13 11.31 283.6

Kevin Kisner 110.97 164.10 11.60 283.6

Kevin Stadler 113.62 168.43 11.20 283.6

Kevin Streelman 115.47 169.53 10.94 283.6

Danny Lee 113.89 168.05 11.01 283.5

Mathew Goggin 112.82 167.40 11.42 283.4

Justin Rose 114.63 167.47 11.99 283.3

Daniel Summerhays 113.02 167.09 10.28 283.2

Fredrik Jacobson 113.47 166.26 9.56 283.2

Pat Perez 115.40 169.33 10.84 283.2

Roland Thatcher 112.64 166.92 12.20 283.2

Stephen Gangluff 114.55 169.97 10.35 283.2

Ben Crane 109.99 163.20 12.29 283.0

Cameron Tringale 114.76 169.63 10.78 283.0

Geoff Ogilvy 114.96 170.40 10.88 283.0

J.J. Killeen 116.26 171.08 8.23 282.9

Brendan Steele 112.26 166.28 12.02 282.8

Miguel Angel Carballo 113.62 168.60 10.16 282.7

Sang-Moon Bae 114.12 168.73 9.33 282.7

Brandt Jobe 115.70 171.65 10.69 282.6

Marc Leishman 115.52 171.26 11.24 282.2

Kyle Reifers 111.59 165.44 11.70 281.8

Tim Herron 112.73 167.17 10.60 281.6

Stewart Cink 115.95 171.13 11.20 281.4

James Driscoll 117.58 173.27 8.75 281.3

Steve Wheatcroft 109.67 162.76 11.61 281.3

Jonas Blixt 111.92 164.16 11.49 281.2

Padraig Harrington 114.92 170.53 10.47 281.2

Tommy Biershenk 109.44 162.21 12.65 281.2

Tom Gillis 113.96 167.07 9.04 281.1

Chad Campbell 112.89 167.23 9.77 281.0

John Huh 111.11 164.87 11.88 281.0

Ian Poulter 110.97 164.73 9.85 280.9

Rod Pampling 112.31 166.09 9.42 280.9

Brandt Snedeker 110.75 164.04 12.61 280.8

Jeff Maggert 106.09 157.48 13.05 280.8

Johnson Wagner 110.58 164.09 10.31 280.8

Matt Every 113.42 167.54 10.98 280.8

Derek Lamely 116.06 172.10 10.75 280.6

Blake Adams 113.65 168.14 10.04 280.5

D.A. Points 110.48 163.95 11.40 280.5

Billy Mayfair 110.08 163.34 13.37 280.4

Matt Bettencourt 113.05 167.89 11.39 280.3

K.J. Choi 109.62 162.04 10.75 280.2

Brendon de Jonge 115.65 170.32 8.57 280.1

Graeme McDowell 112.40 165.25 10.04 280.0

Hunter Haas 111.96 165.31 8.51 280.0

Matt Kuchar 108.13 160.51 11.36 280.0

Ryan Moore 111.51 165.08 10.22 280.0

Robert Allenby 111.62 165.58 11.79 279.9

Marco Dawson 111.22 164.84 10.66 279.8

Ricky Barnes 116.05 170.84 8.44 279.7

Trevor Immelman 118.20 172.33 6.72 279.7

Spencer Levin 110.50 164.05 9.77 279.4

Vaughn Taylor 108.42 161.00 13.30 279.4

George McNeill 115.66 171.40 9.74 279.2

J.J. Henry 114.03 168.60 11.15 279.1

David Hearn 109.74 162.69 14.06 279.0

Y.E. Yang 112.73 166.05 9.38 278.8

Richard H. Lee 109.79 162.97 10.73 278.7

Ted Potter, Jr. 109.70 161.75 9.77 278.7

William McGirt 112.89 167.43 9.80 278.7

Cameron Beckman 109.79 162.39 10.88 278.3

Chris Stroud 111.16 164.80 10.85 278.1

Arjun Atwal 109.72 162.87 11.23 277.8

Kris Blanks 112.19 164.63 10.34 277.7

Alexandre Rocha 109.32 162.34 11.78 277.3

Chez Reavie 109.86 163.06 11.78 277.3

Kevin Na 112.97 165.33 10.04 277.3

Russell Knox 109.50 162.41 10.82 277.2

Kyle Thompson 107.68 159.89 11.65 277.1

Charlie Wi 111.44 164.82 11.15 276.9

Scott Dunlap 110.76 162.39 10.19 276.4

Zach Johnson 107.57 159.21 12.29 276.4

Stuart Appleby 112.43 165.42 9.24 276.3

Brendon Todd 110.66 163.73 10.69 276.2

Sung Kang 109.76 162.70 11.81 276.1

Michael Thompson 111.63 165.53 11.93 276.0

Jim Furyk 109.60 162.12 9.56 275.9

Dicky Pride 109.35 162.21 11.13 275.7

Nathan Green 115.02 169.92 7.63 275.6

Rocco Mediate 107.57 159.75 11.74 275.6

Gary Christian 109.31 162.23 10.54 275.3

Ben Curtis 108.23 160.08 12.00 275.2

Ken Duke 110.93 164.09 8.66 275.2

Tim Clark 104.37 154.88 12.37 275.2

Bob Estes 111.90 165.98 10.02 275.1

Michael Bradley 114.15 169.53 10.24 275.1

David Toms 104.29 154.98 13.99 274.9

Heath Slocum 106.18 157.45 11.72 274.9

Stephen Ames 109.85 161.89 10.38 274.9

Luke Donald 110.69 163.94 11.45 274.7

Patrick Sheehan 107.82 159.98 11.12 274.7

Greg Chalmers 109.83 162.54 9.29 274.6

Jason Bohn 109.76 162.83 10.33 274.4

Brian Davis 105.83 156.96 12.09 274.2

David Mathis 107.65 159.39 10.82 274.1

Justin Leonard 107.33 159.25 11.02 273.5

Bryce Molder 109.28 161.82 10.70 273.0

Mark Wilson 107.55 159.14 12.75 273.0

Brian Gary 104.59 155.17 13.09 272.8

John Mallinger 107.99 160.27 11.66 272.4

Billy Hurley III 109.15 158.94 10.26 270.9

Ryuji Imada 109.89 162.56 10.37 270.9

Jerry Kelly 105.40 155.50 12.64 270.4

Chris DiMarco 107.13 157.41 11.35 270.1

Colt Knost 106.76 157.74 10.76 268.8

Gavin Coles 104.75 154.43 10.55 268.5

Tom Pernice Jr. 107.03 158.41 11.54 268.2

Nick O'Hern 104.66 155.27 11.54 265.7

1Does the estimated regression equation provide a good fit to the data? Explain.

2 In part (b) of a different question , an estimated regression equation was developed using only ball speed to predict the average number of yards per drive. Compare the fit obtained using just ball speed to the fit obtained using ball speed and the launch angle.

The confidence interval for the difference in means

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 15.1; σ = 4.0

P(10 ≤ x ≤ 26) =

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 38; σ = 14

P(50 ≤ x ≤ 70) =

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 6.0; σ = 1.6

P(7 ≤ x ≤ 9) =

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 24; σ = 3.4

P(x ≥ 30) =

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 102; σ = 19

P(x ≥ 90) =

Which one of the following statements is correct about hypothesis testing?

Please provide examples or situations where you can use higher or lower alpha level