1- Nelson Industries manufactures a part for a type of aircraft engine that is becoming obsolete. The sales history for the last 10 years is as follows:

year    sales

Dec-98 945

Dec-99 875

Dec-00 760

Dec-01 690

Dec-02 545

Dec-03 420

Dec-04 305

Dec-05 285

Dec-06 250

Dec-07 210

1. Estimate the regression model for a linear time trend of sales.
2. What is the root-mean-squared error of the linear regression estimates for these 10 years?
3. Using this model, estimate sales for year 11.

Listed below are the top 10 annual salaries​ (in millions of​ dollars) of TV personalities. Find the​ range, variance, and standard deviation for the sample data. Given that these are the top 10​ salaries, do we know anything about the variation of salaries of TV personalities in​ general? 41     39     37     29     17     16     13     10     9.8     9.0 The range of the sample data is ​$ nothing million. ​(Type an integer or a​ decimal.) The variance of the sample data is nothing. ​(Round to two decimal places as​ needed.) The standard deviation of the sample data is ​$ nothing million. ​(Round to two decimal places as​ needed.) Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in​ general?

In a certain city, 30% of the families have a MasterCard, 20% have an American Express card, and 25% have a Visa card. Eight percent of the families have both a MasterCard and an American Express card. Twelve percent have both a Visa card and a MasterCard. Six percent have both an American Express card and a Visa card.

31. Is possession of a Visa card independent of possession of a MasterCard? Why or why not?

32. If a family has a Visa card, what is the probability that it has a MasterCard?

33.Is possession of an American Express card mutually exclusive of possession of a Visa card? Why or why not?

34.What is the probability of selecting a family that has either a Visa card or an American Express card?

35.If a family has a MasterCard, what is the probability that it has a Visa card?

36.What is the probability of selecting a family that has either a Visa card or a MasterCard?

2.The following table contains data on the joint distribution of age(Age​)and average hourly earnings​(AHE​)for 25 to 34​ year-old full-time workers with an educational level that exceeds a high school diploma in 2012. Download the data from the table by clicking the download table icon.A detailed description of the variables used in the dataset is available here

. Use a statistical package of your choice to answer the following questions.

Compute the marginal distribution of

Age.

A.Compute the mean of AHE for Age​ = 31​; that​ is, compute, E( (AHE Age=31)=.

B. Use the law of iterated expectations to compute the mean of AHE​; that is compute E(AHE)

c. Compute the variance of AHE​; that is compute   var(AHE​).

D. Compute the covariance between AHE and Age​; that is compute cov (AHE​, Age​)

F. Compute the correlation between AHE and Age​; that is compute corr(AHE​, Age​)

Find the​ z-score such that the interval within z standard deviations of the mean for a normal distribution contains

a. 34% of the probability

b. 94% of the probability

The weights for newborn babies is approximately normally distributed with a mean of 6.4 pounds and a standard deviation of 1.4 pounds.

Consider a group of 1100 newborn babies:

1. How many would you expect to weigh between 4 and 8 pounds? 

2. How many would you expect to weigh less than 7 pounds? 

3. How many would you expect to weigh more than 6 pounds? 

4. How many would you expect to weigh between 6.4 and 10 pounds? 

How would you use an error component of a time series to know if the time series can be used as a predictor?

In a controlled laboratory environment, independent random samples of 10 adults and 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The study provided the following results:

  Adults     Children

Sample size    10 10

Sample mean (in degrees)   77.5              74.5

Sample variance 4.5    2.5

Which one of the following is the correct 99% confidence interval for the true difference in population mean temperatures that adults and children find most comfortable?

An automobile manufacturer claims that their van has a 46.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van. After testing 140 vans they found a mean MPG of 46.0. Assume the standard deviation is known to be 2.6. Is there sufficient evidence at the 0.02 level that the vans underperform the manufacturer's MPG rating? Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places.

You have a normal population with a mean of 1000 and a standard deviation of 100. Determine the scores associated with the following percentiles:

1. 50%
2. 45%
3. 95%
4. 5%
5. 77%

USE THIS TABLE to practice the Expected Monetary Value (EMV), Expected Opportunity Loss (EOL), and Expected Value of Perfect Information (EVPI). *** Use the .30 for the probability of a Strong Market, .50 for the probability of a Fair Market, and .20 for the probability of a Poor Market. (SHOW YOUR WORK) and show your selections (highlight your best alternative)

In a study of pregnant women and their ability to correctly predict the sex of their​ baby, 58 of the pregnant women had 12 years of education or​ less, and 41.4​% of these women correctly predicted the sex of their baby. Use a 0.01 significance level to test the claim that these women have an ability to predict the sex of their baby equivalent to random guesses. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and conclusion about the null hypothesis. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution. Do the results suggest that their percentage of correct predictions is different from results expected with random​ guesses?

Identify the null and alternative hypotheses. Choose the correct answer below. A. H0​: pequals0.5 H1​: pnot equals0.5 B. H0​: pequals0.414 H1​: pless than0.414 C. H0​: pequals0.5 H1​: pgreater than0.5 D. H0​: pequals0.414 H1​: pnot equals0.414 E. H0​: pequals0.414 H1​: pgreater than0.414 F. H0​: pequals0.5 H1​: pless than0.5

The test statistic is zequals nothing. ​(Round to two decimal places as​ needed.)

The​ P-value is nothing. ​(Round to four decimal places as​ needed.)

Identify the conclusion about the null hypothesis. Do the results suggest that their percentage of correct predictions is different from results expected with random​ guesses? ▼ Reject Fail or to reject H0. There ▼ is or not is sufficient evidence to warrant rejection of the claim that these women have an ability to predict the sex of their baby equivalent to random guesses. The results for these women with 12 years of education or less suggests that their percentage of correct predictions ▼ is not is very different from results expected with random guesses.

Consider the following data, which represent bicycle tire pressures (in psi) for new “road bicycle” wheels shipped to regional bicycle shops.

87, 90, 135, 120, 110, 100, 101, 140, 130, 137, 91, 98, 107, 108, 132

i. Manufacturers are concerned that the bicycle tires should be road safe upon delivery, which means the typical tire pressure should be at most 130 psi. Construct an appropriate pair of hypotheses that could be used to test this.

ii. Explain why a nonparametric approach may be appropriate for this data situation.

iii. By hand, use the Sign Test to evaluate your hypotheses using the data. What is your conclusion?

iv. Reproduce your test using statistical software.

v. Suppose that manufacturers want to ensure that their bicycle tires fall within the range of 80 psi and 130 psi. Can they conclude this from their data?

1- What are the advantages and disadvantages for using doughnut chart?

2- What type of insights can you gain from a contingency table that contains three variables that you cannot gain from a contingency table that contains two variables?

Consider the following simplified financial statements for the Fire Corporation (assuming no income taxes):

The company has predicted a sales increase of 14 percent. It has predicted that every item on the balance sheet will increase by 14 percent as well.

What is the pro forma net income?