Be sure to clearly state your hypotheses in the hypothesis tests and state your conclusions in terms of the problem. Use ?=.?? for all tests.

The following table presents shear strength (in kN/mm) and weld diameters (in mm) for a sample of spot welds.

Diameter Strength

4.2                51

4.4                54

4.6               69

4.8                81

5.0                75

5.2               79

5.4                89

5.6               101

5.8                98

6.0               102

6.Can the least-squares line be used to predict the strength for a diameter of 8 mm? If so, predict the strength. If not, explain why not.

7.For what diameter would you predict a strength of 95 kN/mm?

8.Compute the coefficient of determination and explain what it represents.

9.Compute a 90% confidence interval for the mean shear strength of welds with diameters of 5.1 mm.

10.Compute a 99% prediction interval for the shear strength of particular weld with diameter 5.1 mm.

11.Construct two residual plots (residuals versus the fitted y values and a normal probability plot of the residuals) and discuss what they tell you about the fit of the model and whether the model assumptions are satisfied.

Please solve using Minitab and show step

1. A 2009 sample of New York hotel room prices had an average of $273. Assume this was from a sample of 48 hotels with a sample standard deviation of $72. Construct a 95% confidence interval and report the lower bound for the interval. (Answer to one decimal place and do not include a $ sign).

2.A 2009 sample of New York hotel room prices had an average of $273. Assume this was from a sample of 48 hotels with a sample standard deviation of $72. Construct a 95% confidence interval and report the upper bound for the interval. Your number should be larger than for the previous problem. (Answer to one decimal place and do not include a $ sign).

Question 4

Researchers studied four different blends of gasoline to determine their effect on miles per gallon (MPG) of a car. An experiment was conducted with a total of 28 cars of the same type, model, and engine size, with 7 cars randomly assigned to each treatment group. The gasoline blends are referred to as A,B,C, and D.The MPGs are shown below in the table

Gasoline Miles Per

Blend Gallon

A 26 28 29 23 24 25 26

B 27 29 31 32 25 24 28

C 29 31 32 34 24 28 27

D 30 31 37 38 36 35 29

We want to test the null hypothesis that the four treatment groups have the same mean MPG vs. the alternative hypothesis that not all of the means are equal.

a) Before carrying out the analysis, check the validity of any assumptions necessary for the analysis you will be doing. Write a brief statement of your findings

b) Test the null hypothesis that the four gasoline blends have the same mean MPGs, i.e., Test Ho: ua=ub=uc=ud vs. the alternative hypothesis Ha: not all the means are equal.

c) If your hypothesis test in (b) indicates a significant difference among the treatment groups, conduct pairwise multiple comparison tests on the treatment group means. Underline groups of homogeneous means.

d) Briefly state your conclusions.

( Use IBM SPSS for all calculations)

A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ= 140+# mg/dl and σ = #+1 mg/dl, where # is the last digit of your GCU student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:

1. Once?
2. 8 times?
3. 10 times?

Comment on the relationship between the probabilities observed in (a), (b), and (c).

A medical researcher wants to begin a clinical trial that involves systolic blood pressure (SBP) and cadmium (Cd) levels. However, before starting the study, the researcher needs to know if there is a relationship between SBP and Cd. Below are the SBP and Cd measurements for a sample a participants. What can the researcher conclude with α = 0.05?

a) What is the appropriate statistic?
---Select one--- (na, Correlation, Slope, Chi-Square)
Compute the statistic selected in a):  

b) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =  
Decision:  ---Select one--- (Reject H0, Fail to reject H0)  

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =   ;   ---Select one--- (na, trivial effect, small effect, medium effect, large effect)  

d) Make an interpretation based on the results.

a. There was a significant positive relationship between systolic blood pressure and cadmium levels.

b. There was a significant negative relationship between systolic blood pressure and cadmium levels.

c. There was no significant relationship between systolic blood pressure and cadmium levels.

A tablet PC contains 3217 music files. The distribution of file size is highly skewed with many small files. Suppose the true mean file size of music and video files on the tab, LaTeX: \mu\:=\:2.30μ = 2.30 MB, and also assume that the standard deviation for this population (LaTeX: \sigmaσ )is 3.25 megabytes (MB). If you select a random sample of 50 files.

a. What is the probability that the mean file size of your sample (50 files as described in question 2) is less than 2.5 MB?

b. What is the probability that the mean file size of your sample is greater than 3.0 MB?

Participants enter a research study with unique characteristics that produce different scores from one person to another. For an independent-measures study, these individual differences can cause problems. Briefly explain how these problems are eliminated or reduced with a repeated-measures study

Question 10

:A jar contains 2 red balls, 2 blue balls, 2 green balls, and 3orange balls. Balls are randomly selected, without replacement,until 2 of the same colour are obtained. Calculate the probability thatmore than 3 balls must be selected

An ecologist hypothesizes that birds with longer wing spans use wider tree branches. The ecologist captured male birds, measured their wing span and other characteristics in millimeters, and then marked and released them. During the ensuing winter, the ecologist repeatedly observed the marked birds as they foraged for food on tree branches. He noted the branch diameter on each occasion, and calculated the average branch diameter for each bird in centimeters. The measurement data are below. What can the ecologist conclude with α = 0.01?

a) What is the appropriate statistic?
---Select--- (na, Correlation, Slope, Chi-Square)
Compute the statistic selected in a):  

b) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =  
Decision:  ---Select one--- (Reject H0, Fail to reject H0)

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;   ---Select one--- (na, trivial effect, small effect, medium effect, large effect)

d) Make an interpretation based on the results.

a. There was a significant positive relationship between the wing span of the birds and branch diameter.

b. There was a significant negative relationship between the wing span of the birds and branch diameter.

c. There was no significant relationship between the wing span of the birds and branch diameter.

About 10.8 million gallons of oil were spilled into Alaska's Prince William Sound from the 1989 Exxon Valdez oil spill. A major cleanup effort lasted for three years and removed about 99% of the oil from the water and surrounding beaches. However, a 2007 study estimated that about 70,000 gallons of oil were still in the water and on the beaches and that the amount of oil remaining was decreasing at an annual rate of 4%.

(a)

Write an exponential function expressing the amount of oil in the water

O

from 2007 on as a function of time, with

t = 0

in 2007.

O =

(b)

Use your function to estimate, in gallons, the amount of oil that will remain in the water and on the beaches in 2025. (Round your answer to the nearest integer.)

gal

Use your function to estimate, in gallons, the amount of oil that will remain in the water and on the beaches in 2040. (Round your answer to the nearest integer.)

gal

(c)

Some environmentalists feel that the spillage will be effectively "gone" once the amount of oil remaining is less than 1000 gallons. How long will this take in years, based on your model? (Round your answer to the nearest integer.)

yr

(d)

Assuming that the same decay rate has been in effect since the major cleanup efforts ended in 1992, estimate how much oil, in gallons, was in the water and on the beaches at that time. (Round your answer to the nearest integer.)

gal

1. What is our t-critical if we have a sample of 35 people and want to use an alpha of .05, where our hypothesis specifies direction?

2. What is our t-critical if our sample has 96 people, we want to use an alpha of .01, and do not have hypotheses which include direction?

3. Given a sample of 68 women, with an estimated standard error of 2.5 and a sample mean of 15, construct a confidence interval for a one-tailed test with an alpha of .05.

4. Franklin conducts a survey as a part of his PSYC 406 research project, trying to determine if having individuals watch romantic comedies affects their mood. In his survey he uses a measure of mood, which contains a 7 point scale ranging from 1 – 7. His sample includes 45 people, with a SS = 1, 219 and a mean rating on the survey of a 4.57. Using an alpha = .05, answer the following questions.
   1. Write out his null and alternative hypotheses.

2. What is his t-critical value(s)?

3. What is the estimated standard error?

4. Compute the t-statistic.

5. What is the effect size?

6. Make a decision regarding the null and provide a conclusion in proper notation.

5. Zaxby’s wants to know if their advertising during the NCAA tournament altered the sales of their wings and things plate that was being shown in their commercials. They decide to use the location on 74 as a test location. On an average day they sell 239 wings and things plates. Taking a sample of 17 days during the tournament, they find that they sold 250 wings and things plates on average, with a standard deviation of 16 plates. Using an alpha = .05, answer the following questions.
   1. What are their null and alternative hypotheses?

2. What is their t-critical value(s)?

3. What is the estimated standard error?

4. Compute the t-statistic.

5. What is the effect size?

6. Make a decision regarding the null and provide a conclusion in proper notation.

A manufacturer produces widgets whose lengths are normally distributed with a mean of 9.2 cm and standard deviation of 0.9 cm.
A. If a widget is selected at random, what is the probability it is greater than 9.3 cm?  
B. What is the standard deviation of the average of samples of size 37?  
C. What is the probability the average of a sample of size 37 is greater than 9.3 cm?  
Round answer to four decimal places.

Cards are dealt without replacement from a standard deck.

(a) Find the conditional probability that the second card is a club given that the first card

is club.

(b) Find the conditional probability that the second card is a club given that the second-to-

last card is a club.

(c) Find the conditional probability that the first card is a club given that none of the next

five cards are clubs.

(d) Find the expected number of clubs that appear before the king of diamonds.

You should explain the confidence intervals you create along with explanations of the meaning of your answers and business implications for each problem.

Scenario:

You have been asked once again to study the mean tuition at private universities throughout the United States. You will also again study the proportions of universities throughout the United States that regularly award more than 50% of their students some form of financial aid. The specific questions you will be asked to answer are stated below. In addition, appropriate sample data for the studies you will be accomplishing is given below. Answer the following questions concerning the situations posed.

The organization for which you are working in your study of private university tuition has been quite impressed with your work. Its CEO has a relative who works for the Major-League Baseball Players’ Union. Your services and abilities have been recommended to union leadership. You have been asked to perform a study that will result in a comparison of the average salaries per player for major league baseball teams. This information will be needed as historical data to be used in upcoming labor negotiations. The average player salary data for two recent years for all 30 major league baseball teams is shown below in appendix two. At the 1% level of significance, has the average player salary increased from the first year to the second year? For the purposes of the study, you may assume that this data is sample data drawn from a much larger population of teams. Once again, should the procedure you choose to accomplish this task allow for it, construct a 99% confidence interval for the difference in the mean salary per player from year one to year two. Explain the meaning of this interval.

Appendix Two (Salaries)

Year

Team Two One New York Yankees $7,663,361 $6,862,918

Philadelphia Phillies $4,055,455 $3,393,916

Boston Red Sox $4,581,533 $4,196,967

Chicago White Sox $3,458,400 $4,501,832

Chicago Cubs $4,630,693 $4,675,883

St. Louis Cardinals $4,416,937 $3,342,380

San Francisco Giants $2,899,400 $2,391,955

New York Mets $3,765,567 $3,916,288

Detroit Tigers $4,434,909 $4,148,959

Atlanta Braves $3,680,180 $2,693,161

Minnesota Twins $2,664,878 $1,934,886

Los Angeles Dodgers $4,334,605 $4,371,154

Los Angeles Angels $4,223,942 $4,110,408

Texas Rangers $2,402,506 $1,991,413

Baltimore Orioles $1,684,182 $1,995,760

Tampa Bay Rays $2,297,365 $1,594,997

Colorado Rockies $2,926,721 $2,554,035

Seattle Mariners $3,377,771 $3,270,666

Cincinnati Redlegs $2,153,075 $1,748,586

Milwaukee Brewers $2,937,499 $3,562,592

Toronto Blue Jays $1,825,987 $2,829,826

Houston Astros $3,464,718 $3,610,588

Oakland Athletics $1,469,254 $1,740,764

Washington Nationals $1,685,950 $1,349,305

Kansas City Royals $2,621,263 $1,820,423

San Diego Padres $ 959,165 $1,720,590

Arizona Diamondbacks $2,168,853 $3,015,390

Florida Marlins $1,327,968 $ 868,261

Cleveland Indians $2,007,420 $1,905,804

Pittsburgh Pirates $ 790,167 $1,201,117