Let X and Y be two independent random variables such that X + Y has the same density as X. What is Y?

A marketing researcher predicts that college students will be more likely to purchase tickets for... A marketing researcher predicts that college students will be more likely to purchase tickets for the next football home game if their team won (vs. lost) the last game. The researcher asked 6 WSU students their willingness to purchase tickets (1= not likely at all, 7=very likely) and 6 EWU students their willingness to purhcase tickets (1=not likely, 7=very likely) (WSU won the game in the 2018 season)

WSU: 7 6 5 7 2 4

EWU: 6 5 6 5 1 6

In answering the questions, make sure to write down the following 7 steps.

Step 1. Establish null and alternative hypotheses (as a sentance and formula)

Step 2: Calculate the degrees of freedom

Step 3: calculate the t-critical using critical t-table

Step 4: calculate the Sum of Squares deviation

Step 5: Calculate t-obtained

Step 6: Specify the critical value and the obtained value on a t-distribution curve.

A personnel specialist with a large accounting firm is interested in determining the effect of seniority on hourly wages for secretaries. She selects at random 10 secretaries and compares their years with the company (X) and hourly wages (Y).

x	y
0	12
2	13
3	14
6	16
5	15
3	14
4	13
1	12
1	15
2	15

• Calculate the regression slope and intercept (2 points).
• Predict the hourly wage of a secretary that has been with the company for four years (1 point).
• Find the coefficients of determination and nondetermination, and interpret both values (2 points).

A random sample of 200 books purchased at a local bookstore showed that 72 of the books were murder mysteries. Let p be the true proportion of books sold by this store that is murder mystery. Construct a confidence in terval with a 95% degree of confidence.Compute the following:

a.Point estimate

b.Critical value

c.Margin of error

d.Confidence interval

e.Interpretation(confidence statement).

What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 54 college students were surveyed and r = 11 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05. (a) What is the level of significance? 0.05 Correct: Your answer is correct. State the null and alternate hypotheses. H0: p = 0.24; H1: p > 0.24 H0: p = 0.24; H1: p ≠ 0.24 H0: p ≠ 0.24; H1: p = 0.24 H0: p = 0.24; H1: p < 0.24 Correct: Your answer is correct. (b) What sampling distribution will you use? The Student's t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5. Correct: Your answer is correct. What is the value of the sample test statistic? (Round your answer to two decimal places.) -0.04 Incorrect: Your answer is incorrect. (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) 0.24 Incorrect: Your answer is incorrect.

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013). The numbers in Table 3 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Is there enough evidence to show that the activity and the time period are independent for dolphins? Why or Why not? Test at the 1% level.

Activity	Morning	Noon	Afternoon	Evening	Row Total
Travel	6	6	14	13	39
Feed	28	4	0	56	88
Social	38	5	9	10	62
Column Total	72	15	23	79	189

In 2003 and 2017 a poll asked Democratic voters about their views on the FBI. In​ 2003, 42​% thought the FBI did a good or excellent job. In​ 2017, 64​% of Democratic voters felt this way. Assume these percentages are based on samples of 1200 Democratic voters.

1) Can we​ conclude, on the basis of these two percentages​ alone, that the proportion of Democratic voters who think the FBI is doing a good or excellent job has increased from 2003 to​ 2017? Why or why​ not?

Select one:

a. No. Although a lesser percentage is present in the​ sample, the population percentages could be the same or even reversed.

b. No. Since a greater percentage is present in the​ sample, we cannot conclude that a lesser percentage of Democratic voters who think the FBI is doing a good or excellent job is present in the population.

c. No. Although a lesser percentage is present in the​ sample, the population percentages could be the​ same, but could not be reversed.

d. Yes. Since a lesser percentage is present in the​ sample, a lesser percentage of Democratic voters who think the FBI is doing a good or excellent job is present in the population.

2) Construct a 95​% confidence interval for the difference in the proportions of Democratic voters who believe the FBI is doing a good or excellent​ job, p1−p2. Let p1 be the proportion of Democratic voters who felt this way in 2003 and p2 be the proportion of Democratic voters who felt this way in 2017.

Select one:

a. (0.39, 0.45)

b. (-0.259, -0.181)

c. (-0.24, -0.20)

d. (0.63, 0.65)

The mean operating cost of a 737 airplane is $2071 per day. Suppose you take a sample of 49 of these 737 airplanes and find a mean operating cost of $2050 with a sample standard deviation of $106.

A.) what is the probability that a 737 will have an operating cost that is greater than the sample mean you have found? (show work)

B.) what is the probability that a plane would have an operating cost that is between $2050 and 2088.60 per day? (show work)

An educational psychologist wants to know if length of time and type of training affect learning simple fractions. Fifth graders were randomly selected and assigned to different times (from 1 to 3 hours) and different teaching conditions (old method vs. meaningful method). All students were then tested on the "fractions" subtest of a standard arithmetic test. What can the psychologist conclude with α = 0.01?

	Time
Train	one hr	two hrs	three hrs
old	5 6 7	6 7 7	8 9 10
meaningful	6 7 11	9 10 11	7 9 10

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Train: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Time: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Interaction: p-value =  ; Decision:

A simple random sample of 60 items resulted in a sample mean of 75. The population standard deviation is 17.

Compute the 95% confidence interval for the population mean (to 1 decimal).

Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).

What is the effect of a larger sample size on the margin of error?

Consider a game of chance consisting of a single trial with exactly two outcomes, which from a players perspective we will call "win" and "lose." To play the game, a player must wager an amount, which we will denote by a. If the player loses the game, a player loses their wager. If the player wins the game, then they keep their wager and they win $1.00. Denote the probability by p, where 0 < p < 1. Let the random variable X denote the amount won by the player.

A) Find the sample space of the random variable X.

B) Find the pmf of the distribution of the random variable X.

C) Compute the expression for E(X), the expected value of X.

D) A game is said to be fair if the expected amount won is 0. For what value of a, the amount wagered, would the game be described as a fair game?

E) For what vaules of a is E(X) >0?

F) For what values of a is E(X) <0?

G) Suppose a person is only willing to play if their expected amount won is non negative. For what values of a would this person be willing to play, and what values of a would this person not be willing to play?

1. Following a normal probability distribution with a mean of 200 and a standard deviation of 10, 95 percent  of the population will be between:

		200 and 220
		180 and 220
		180 and 200
		less than 180

3. A family of four spends an average of $1000 per month with a standard deviation of $50.  This spending follows a normal continuous distribution.  

What is the probability that a family will spend more than $1050 in a month?  (answer to 3 decimal places)

5. If two events, A and B, are mutually exclusive, then P(A or B) = P(A) + P(B) - P(A&B)

True

False

6. A coin is tossed 8 times.  It is a fair coin with 2 sides, heads and tails.  What is the probability that in 8 tosses, 7 or less will be flipped?

		0.996
		0.004
		1
		0.5

7. Following a normal probability distribution with a mean of 200 and a standard deviation of 10, 68 percent  of the population will be between:

		170 and 230
		190 and 210
		180 and 220
		Greater than 200

1. What is meant by a “null” hypothesis?
2. How do you test a null hypothesis?
3. What are alternate hypotheses?  
4. What are p-values?
5. Explain "significance level."

This is for business statistics

An experiment was conducted to see the effectiveness of two antidotes to three different doses of a toxin. The antidote was given to a different sample of participants five minutes after the toxin. Twenty-five minutes later the response was measured as the concentration in the blood. What can the researchers conclude with α = 0.01?

	Dose
Antidote	5	10	15
1	0.6 1.1 1.1	2.1 1.5 6.2	3.1 4.1 5.9
2	1.1 1.2 1.1	1.7 1.3 1.5	2.1 3.1 2.1

Compute the corresponding effect size(s) and indicate magnitude(s).
Antidote: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Dose: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is an antidote difference in blood concentration.There is no antidote difference in blood concentration.    

There is a dose difference in blood concentration.There is no dose different in blood concentration.    

There is an antidote by dose interaction in blood concentration.There is no antidote by dose interaction in blood concentration.    

A large sports supplier has many stores located world wide. A regression model is to be constructed to predict the annual revenue of a particular store based upon the population of the city or town where the store is located, the annual expenditure on promotion for the store and the distance of the store to the center of the city.

Data has been collected on 30 randomly selected stores: (AT BOTTOM)

Find the multiple regression equation using all three explanatory variables. Assume that x₁ is population, x₂ is annual promotional expenditure and x₃ is distance to city center. Give your answers to 3 decimal places.

a) y^ = BLANK + BLANK population + BLANK promo. expenditure + BLANK dist. to city

e)The value of R² for this model, to 3 decimal places, is equal to

f)The value of s for this model, to 3 decimal places, is equal to

g)Construct a new multiple regression model by removing the variable distance to city center. Give your answers to 3 decimal places.

The new regression model equation is:

y^ = + population + promo. expenditure

At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis A) Is B) is not rejected.

c)The explanatory variable that is most correlated with annual revenue is:

population
promotional expenditure
distance to city

d)The explanatory variable that is least correlated with annual revenue is:

population
promotional expenditure
distance to city

H) In the new model compared to the previous one, the value of R² (to 3 decimal places) is:

increased
decreased
unchanged

i)In the new model compared to the previous one, the value of s (to 3 decimal places) is:

increased
decreased
unchanged

Annual revenue ($) (× 1000)	Population (× 1000)	Annual promotional expenditure ($) (× 100)	Distance to city center (mi)
195	124	142	19
104	90	64	9
294	459	138	6
316	667	95	19
228	189	158	18
406	849	74	7
247	284	177	19
204	267	113	19
60	46	100	9
539	918	172	15
575	942	175	8
326	677	90	14
275	479	129	1
470	834	168	1
308	435	129	5
318	475	178	7
512	915	95	18
153	183	173	11
219	266	134	16
443	687	197	15
225	177	184	1
233	192	185	18
303	612	93	5
507	981	93	16
487	923	138	2
432	963	44	17
180	138	165	10
448	820	55	11
461	719	156	10
97	48	115	19