4) Suppose that there are two products under purchase consideration. Both products have       similar other characteristics, but we are not sure about their respective warm-up       variances. Are they equal or not? A sample of 64 items from product 1, yielded a       variance of 16, while a sample of 36 items from product 2, yielded a variance of 12. a) Test this claim at both α = 0.05 and α = 0.01? b) Construct 95% and 99% confidence Intervals on the appropriate population       parameter. c) Are the results in (a) and (b) the same? Why or why not? BE SEPCIFIC!  

If x is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases:

(a)  n=4,p=0.4n=4,p=0.4
μ=
σ2=
σ=

(b)  n=3,p=0.2n=3,p=0.2
μ=
σ2=
σ=

(c)  n=3,p=0.6n=3,p=0.6
μ=
σ2=
σ=

(d)  n=6,p=0.7n=6,p=0.7
μ=
σ2=
σ=

1. Here is a link to a data set comparing proficiency in a second language to the density of grey matter in the human brain.

What is the correlation coefficient for these data? Use either the =correl(array1,array2) formul in excel, or the correlation feature in the Data Analysis ToolPak Add-in for Excel to determine the correlation coefficient.

Report your answer to four decimal places.

A. Based on the correlation analysis performed on the density of grey matter and proficiency in a second language, which of the following statements are reasonable conjectures?

(select all correct answers)

Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to influence this stock price are return on average equity (X1) and annual dividend rate (X2). The stock price, returns on equity, and dividend rates on a randomly selected day for several electric utility stocks are provided below.

a) Use Excel to develop the equation of the regression model.Comment on the regression coefficients. Determine the predicted value of y for x1=12.1 and x2 = 3.18

b) Study the ANOVA table and the ratios and use these to discuss the strengths of the regression model and the predictors. Does this model appear to fit the data well? Use alpha = 0.05.

C) Comments on the overall strength of the regression model in light of se, R2, and adjusted R2.

3. A device runs until either 2 components fails, at which the device stops running. Let X and Y be the lifetimes in hours of the first and second component, respectively. The joint probability density function of the lifetimes is:

f(x,y) = { (x+y)/27 : 0 < x < 3, 0< y < 3

{ 0

a) Find the marginal probability density function of X and the marginal probability density function of Y.

b) Are X and Y independent? Why or why not?

c) Find the conditional density of X given that Y = y

d) Find the expected value of X given that Y =1/4

Please show your work, I have an exam tomorrow, thank you!

a-What is the shape of the sampling distribution for the parameter estimates from regression?

b-Speak generally about the process of testing the null hypothesis in the regression context.

(1)The following two claims are similar to the claim in the triangle problem discussed in lecture, but there are subtle differences. Either prove or disprove each claim.

(a) Let T(n) be: C(n, 3) triangles are formed by n lines in the plane if no three of the lines intersect at a single point. ∀n ∈ N, n ≥ 3, T(n).

(b) Let R(n) be: C(n, 3) triangles are formed by n non-parallel lines in the plane. ∀n ∈ N, n ≥ 3, R(n).

Create a Normally (Gaussian) distributed random variable1 X with a mean µ and standard deviation σ.

• [20] Create normally distributed 50 samples (Y) with µ and σ, and plot the samples.

• [20] Create normally distributed 5000 samples (X) with µ and σ, and (over) plot the samples.

• [20] Plot the histogram of random variable X and Y. Do not forget to normalize the histogram.

• [35] Plot the Gaussian PDF and its CDF function over the histogram of random variables Y and X.

Do not forget, interpreting the results is the key to properly learn!!

A random sample is drawn from a normally distributed population with mean μ = 18 and standard deviation σ = 2.3. [You may find it useful to reference the z table.]

b. Calculate the probabilities that the sample mean is less than 18.6 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

If you were the manager of a big company, please provide a scenario/or an application that you would use one or combinations of these two techniques( choose from descriptive statistics, graphs, one sample test, two samples test , ANOVA, two-way ANOVA) to help you in the decision making process.

20- The thicknesses of 73randomly selected linoleum tiles were found to have a variance of 3.14 . Construct the 90% confidence interval for the population variance of the thicknesses of all linoleum tiles in this factory. Round your answers to two decimal places.

Step 1 of 1:

On an ostrich farm, the weights of the birds are found to be normally distributed. The weights of the females have a mean 78.6 kg and a standard deviation of 5.03 kg. The weights of the males have a mean 91.3 kg and a standard deviation of 6.29 kg. Find the probability that a randomly selected: Male will weight less than 80 kg. Female will weight less than 80 kg. Female will weigh between 70 and 80 kg. 20% of females weigh less than k kg. Find k. The middle 90% of the males weigh between a kg and b kg. Find the values of a and b kg.

The following data come from a study designed to investigate drinking problems among college students. In 1983, a group of students were asked whether they had ever driven an automobile while drinking. In 1987, after the legal drinking age was raised, a different group of college students were asked the same question. SHOW EXCEL CODES

Drove While Drinking Year

1983 1987 Total

Yes 1250 991 2241

No 1387 1666 3053

Total 2637 2657 5294

A. Use the chi-square test to evaluate the null hypothesis that population proportions of students who drove while drinking are the same in the two calendar years.

B. What do you conclude about the behavior of college students?

C. Again test the null hypothesis that the proportions of students who drove while drinking are identical for the two calendar years. This time, use the method based on the normal approximation to the binomial distribution that was presenting in Section 14.6. Do you reach the same conclusion?

D. Construct a 95% confidence interval for the true difference in population proportions.

E. Does the 95% confidence interval contain the value 0? Would you have expected it to?

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged

14371437

referee​ calls, with the result that

431431

of the calls were overturned. Women challenged

745745

referee​ calls, and

227227

of the calls were overturned. Use a

0.010.01

significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis​ test?

A.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

B.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

C.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

D.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

E.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

F.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

Identify the test statistic.

zequals=negative . 23−.23

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=. 818.818

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is

greater than

the significance level of

alphaαequals=0.010.01​,

so

fail to reject

the null hypothesis. There

is not sufficient

evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

b. Test the claim by constructing an appropriate confidence interval.

The

9999​%

confidence interval is

nothingless than<left parenthesis p 1 minus p 2 right parenthesisp1−p2less than<nothing.

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits

▼

do not include

include

​0, there

▼

does

does not

appear to be a significant difference between the two proportions. There

▼

is not sufficient

is sufficient

evidence to warrant rejection of the claim that men and women have equal success in challenging calls.

c. Based on the​ results, does it appear that men and women may have equal success in challenging​ calls?

A.

The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that women have more success.

B.

The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.

C.

The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that men have more success.

D.

There is not enough information to reach a conclusion.