Suppose you are interested in bidding on a parcel of land and you know that one other bidder is interested. The seller has announced that the highest bid will be accepted. The other competitor’s bidding price for the land will vary evenly from $72,000 to $85,500.

1. Let B be the competitor’s bid for the parcel of land. What are the distribution and parameter(s) of B?

2. What is expected value and standard deviation of the competitor’s bid?

3. What is the probability that the competitor’s bid will be less than $80,000?

4. What values mark the middle 50% of the competitor’s bids?

5. You and the competitor each put in a sealed bid (i.e. you do not know the competitor’s bid and he does not know yours). Suppose that you bid $79,000. What is the probability that your bid will be accepted? (i.e. that yours will be higher than the competitor.)

6. The competitor has hinted that he will not go higher than $82,750. What is the probability that his actual bid is above $80,200?

Directions: Use the following information to complete the assignment. While APA format is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center.

A researcher randomly assigns 33 subjects to one of three groups. Group 1 receives technical dietary information interactively from an on-line website. Group 2 receives the same information from a nurse practitioner, while Group 3 receives the information from a video tape made by the same nurse practitioner.

The researcher looked at three different ratings of the presentation; difficulty, usefulness, and importance to determine if there is a difference in the modes of presentation. In particular, the researcher is interested in whether the interactive website is superior because that is the most cost-effective way of delivering the information.

1. Run the appropriate analysis of the data and interpret the results.
2. How could this study have been done differently? Why or why not would this approach be better?

According to a Field Poll conducted, 79% of adults (actual results are 400 out of 506 surveyed) feel that "education and our schools" is one of the top issues facing the state. We wish to construct a 90% confidence interval for the true proportion of adults who feel that education and the schools is one of the top issues facing the state. Find a 90% confidence interval for the population proportion. Round your answers to three decimal places.

An email was randomly sent out to 150 people of various ages. I believe that more than 15% of the people being asked support the "Brand X" motorcycle. The people were asked: Out of the brands listed below, what is your preferred brand of motorcycle. Please reply with the alpha number in the subject line.

A) Honda

B)Yamaha

C) Indian

D) Harley Davidson

E) Kawasaki

F) Ducati

Results:

*Successes (x) (i.e. in for of Brand “X” = D = Harley Davidson) = 31 in favor of

*Sample size (n) = 150

SOLVE: (State hypothesis, Z-stat, rejection region, P-Value, Classic approach, reasoning)

Suppose a Department Chair randomly selects 5 new teaching assistants from a total of 20 applicants - 11 boys and 9 girls. Let x be the number of girls who are hired. Find the mean and standard deviation of random variable x.

(a) μ = 2.75 and σ = 0.9770

(b) μ = 2.25 and σ = 0.9884

(c) μ = 2.75 and σ = 0.9884

(d) μ = 2.25 and σ = 0.9770

Consider the following hypotheses:

H₀: p ≥ 0.48

H_A: p < 0.48

Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

1. Use the data analysis package to develop the regression equation.
2. What is the r²?  And what is the standard error?  What do they mean in this example?
3. What does the slope of the line represent in this example?  Use a sentence or two to explain this.
4. What is the 95% confidence interval for the parameter β₁ ?  At the significance level of 5%, can you reject the hypothesis that β₁ = 0?

17. You run a hypothesis test to see whether the average price of gas is higher than the reported value of $2.53. You find a p-value of .001 and reject Ho. a. Which type of error could you be committing here, Type 1 or Type 2? 18. In a jury trial, the jury makes a decision, and they could be right or wrong. Describe how a type 1 error could happen in this situation, and how a type 2 error could happen in this situation. Which error do you believe is worse to commit and why? (This is just your own opinion.) 21. Bob’s local pizza place claims it delivers pizzas in 30 minutes on average. Bob is convinced it’s more than that. He does a hypothesis test and gets a p-value of .001. a. What does Bob conclude? b. If Bob made the wrong conclusion what error did he make? c. What would be the impact of his error?

Use the following data to: draw a scatter plot, find the coefficient correlation, find the regression line, predict y' for x =90.

First Test - X Final test Y

73 70

86 80

93 96

92 85

72 68

65 68

58 62

75 78

Assume that IQ scores for a certain population are approximately normally distributed. TotestH0 :μ=110againstH1 :μ̸=110,wetakearandomsampleofsizen=16from this population and observe x ̄ = 113.5 and s = 10. Do the test with significance level α = 0.05.

(a) Find the test statistic.
(b) Find the critical value from the t-table. (c) Do we accept or reject H0?

(d) Construct the confidence interval related to the test. What is your decision based on the confidence interval?

According to data from the Tobacco Institute Testing Laboratory, a certain brand of cigarette contains an average of 1.4 milligrams of nicotine. An advocacy group questions this figure, and commissions an independent test to see if the the mean nicotine content is higher than the industry laboratory claims.
The test involved randomly selecting n=15n=15 cigarettes, measuring the nicotine content (in milligrams) of each cigarette. The data is given below.

1.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.51.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.5

(a) Do the data follow an approximately Normal distribution? Use alpha = 0.05.  ? yes no

(b) Determine the PP-value for this Normality test, to three decimal places.
P=P=

(c) Choose the correct statistical hypotheses.
A. H0:X¯¯¯¯>1.4,HA:X¯¯¯¯<1.4H0:X¯>1.4,HA:X¯<1.4
B. H0:X¯¯¯¯=1.4,HA:X¯¯¯¯<1.4H0:X¯=1.4,HA:X¯<1.4
C. H0:μ>1.4,HA:μ<1.4H0:μ>1.4,HA:μ<1.4
D. H0:μ=1.4HA:μ>1.4H0:μ=1.4HA:μ>1.4
E. H0:μ=1.4,HA:μ≠1.4H0:μ=1.4,HA:μ≠1.4
F. H0:X¯¯¯¯=1.4,HA:X¯¯¯¯≠1.4H0:X¯=1.4,HA:X¯≠1.4


(d) Determine the value of the test statistic for this test, use two decimals in your answer.
Test Statistic =

(e Determine the PP-value for this test, to three decimal places.
P=P=

(f) Based on the above calculations, we should  ? reject not reject  the null hypothesis. Use alpha = 0.05

Ocean currents are important in the studies of climate change as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, new guinea, and other islands. X represent the number of days to recovery of a drift bottle after release and why represent the distance from point of release to point of recovery in km/100. The following data are taken from the reference by professor E.A. Kay, University of Hawaii.

x days 74 79 34 97 208

y km/100 14.6 19.5 5.3 11.6 35.7

Test slope in regression use significance level of 0.05

Find a confidence interval

Let X1, X2, X3, X4 denote 4 independent observations from a distribution with density f(x;theta)=(1+theta)x^theta, if 0<=x<=1; 0 Otherwise.. What is the form of the LRT critical regoon for testing H0:theta =2 versus H1:theta=5

ANSWER ALL PARTS USE A TI84. All other methods give the wrong answer

The following is a chart of 25 baseball players' salaries and statistics from 2016.

In order to have correlation with 95% confidence (5% significance), what is the critical r-value that we would like to have?  

(Round to three decimal places for all answers on this assignment.)

RBI vs. Salary

Complete a correlation analysis, using RBI's as the x-value and salary as the y-value.

Correlation coefficient:

Regression Equation: y=

Do you have significant correlation? Select an answer Yes No

HR vs. Salary

Complete a correlation analysis, using HR's as the x-value and salary as the y-value.

Correlation coefficient:

Regression Equation: y=

Do you have significant correlation? Select an answer Yes No   

AVG vs. Salary

Complete a correlation analysis, using AVG as the x-value and salary as the y-value.

Correlation coefficient:   

Regression Equation: y=

Do you have significant correlation? Select an answer Yes No

Prediction

Based on your analysis, if you had to predict a player's salary, which method would be the best? Select an answer Regression equation with RBI's Regression equation with HR's Regression equation with AVG The average of the 25 salaries

Using that method, predict the salary for Mike Trout. His stats were:

RBI: 100

HR: 29

AVG: 0.315

Based on your analysis, his predicted salary would be: $_____________ million  

His actual salary was $16.083 million.

2.3) A starting lineup in basketball consists of two guards, two forwards, and a center.

(a) A certain college team has on its roster four centers, four guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.]

(b) Now suppose the roster has 4 guards, 5 forwards, 4 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 15 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)