At a confidence level of 95% a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the sample size had been larger and the estimate of the population proportion the same, this 95% confidence interval estimate as compared to the first interval estimate would be

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data.

(a) Compute Σx, Σx²,  Σy, Σy².

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.)

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)

Use the intervals to compare the two funds.

75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.75% of the returns for the stock fund fall within a narrower range than those of the balanced fund.     25% of the returns for the balanced fund fall within a narrower range than those of the stock fund.25% of the returns for the stock fund fall within a wider range than those of the balanced fund.

(d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.)

Use the coefficients of variation to compare the two funds.

For each unit of return, the stock fund has lower risk.For each unit of return, the balanced fund has lower risk.     For each unit of return, the funds have equal risk.

If s represents risks and x represents expected return, then s/x can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain.

A smaller CV is better because it indicates a higher risk per unit of expected return.A smaller CV is better because it indicates a lower risk per unit of expected return.     

Using the data in RDCHEM.RAW, the following equation was obtained by OLS:
\ rdintens = 2.613 + .00030sales + .0000000070sales2
(.429) (.00014) (.0000000037)
n = 32, R2 = .1484
i) At what point does the marginal effect of sales on rdintens become negative?
ii) Would you keep the quadratic term in the model? Explain.
1
iii) Define salesbil as sales measured in billions of dollars: salesbil = sales 1,000. Rewrite the estimated equation with salesbil and salesbil2 as the independent variables. Be sure to report standard errors and the R-squared. [Hint: Note that salesbil2 = sales2 (1,000)2 .]
iv) For the purpose of reporting the results, which equation do you prefer?

Given the statistics below, what is the appropriate analysis, the test statistic, and the associated effect size?

Sample size: 60.
Sample mean: 1080.
Sample standard deviation: 60.
Population mean: 1000.

According to government data, 46% of employed women have never been married. Rounding to 4 decimal places, if 15 employed women are randomly selected:

a. What is the probability that exactly 2 of them have never been married?

b. That at most 2 of them have never been married?

c. That at least 13 of them have been married?

we toss a fair coin 100 times. What is the probability of getting more than 30 heads?

1. Nine samples of PVC pipe of equal wall thickness are tested under three temperature conditions to failure, yielding the results shown below. Research questions: Is mean burst strength affected by temperature level? Is there an “ideal” temperature level? Explain. You will need to enter the data into Minitab.

• At the 0.05 level of significance, determine if there is a difference mean burst strength by temperature level. State your hypotheses and show all 7 steps clearly.
• Use Levene’s test to determine if the assumption of homogeneity of variances is valid. Give the hypotheses, test statistic, p-value, decision and conclusion. Use the 0.05 level of significance.  
• Verify with Minitab by attaching or including relevant output.

Please show your steps on Mini Tab

1A. Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the probabilities below. (Round all answers to four decimal places.)

(a) P(z < 0.1) =

(b) P(z < -0.1) =

(c) P(0.40 < z < 0.84) =

(d) P(-0.84 < z < -0.40) =

(e) P(-0.40 < z < 0.84) =

(f) P(z > -1.26) =

(g) P(z < -1.49 or z > 2.50) =

1B. Find the following probabilities for X = pulse rates of group of people, for which the mean is 76 and the standard deviation is 8. Assume a normal distribution. (Round all answers to four decimal places.)

(a) P(X ≤ 68).


(b) P(X ≥ 82).


(c) P(56 ≤ X ≤ 92).

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.