The tensile strength, X, of a tungsten component is normally distributed with a mean of 546 grams per square centimeter (gscm) and a standard deviation of 50 gscm.

e) What is the 97.1st percentile of tensile strength of our tungsten component in gscm?

f) Suppose we make 3 independent strength measurements of tungsten components. What is the probability that all 3 measurements are at least 500?

g) What is the probability that X is greater than 525 given that X is greater than 500?

h) Suppose X1,X2,,Xk are k independent strength measurements of tungsten components. Let Xbar be the mean of those k values. How large must k be so the variance of the distribution of Xbar equals .8?

3) The following observations are given for two variables.

Y: 5,8,18,20,22,30,10,7

X:2,12,3,6,11,19,18,9

Compute and interpret the sample covariance for the above data.

Compute the standard deviation for x.

Compute the standard deviation for y.

Compute and interpret the sample correlation coefficient.

Let X1, X2, X3 be independent having N(0,1). Let Y1=(X1-X2)/√2, Y2=(X1+X2-2*X3)/√6, Y3=(X1+X2+X3)/√3. Find the joint pdf of Y1, Y2, Y3, and the marginal pdfs.

1) null hypothesis

2) alternative hypothesis

3) where the region of rejection lies (upper tail, lower tail, both tails)

4) the test that is to be used

5) the degrees of freedom

6) the critical value of the test statistic

7) the computed value of the test statistic

8) the statistical decision (whether the null hypothesis is rejected or not)

9) the p-value

10) the assumptions you made in your work

Now, finally - Here is the question:

Trail mix is sold in individual pouches labeled as containing 8 ounces by weight. The weights of 40 pouches are measured (using a tared scale so that only the weight of the trail mix is measured). The sample mean is found to be 8.5 ounces. The sample standard deviation is calculated to be 0.4 ounces. At 95% confidence, is there evidence that the mean weight per pouch is different from 8 ounces?

A research center project involved a survey of 843 internet users. It provided a variety of statistics on internet users.

(a) The sample survey showed that 90% of respondents said the internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally. (Round your answers to four decimal places.)

(b) The sample survey showed that 71% of internet users said the internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends. (Round your answers to four decimal places.)

(c) Fifty-seven percent of internet users have seen an online group come together to help a person or community solve a problem, whereas only 25% have left an online group because of unpleasant interaction. Develop a 95% confidence interval for the proportion of internet users who say online groups have helped solve a problem. (Round your answers to four decimal places.)

Please respond with at least 175 words. What are a one tail and a two tailed test. Why are they important and what are their differences?

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).