You wish to test the following claim ( H a ) at a significance level of α = 0.05 . H o : μ = 65.3 H a : μ ≠ 65.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 106 with mean ¯ x = 62.8 and a standard deviation of s = 16.2 . What is the test statistic for this sample? (Report answer accurate to two decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 65.3. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 65.3. The sample data support the claim that the population mean is not equal to 65.3. There is not sufficient sample evidence to support the claim that the population mean is not equal to 65.3.

6. Tudor brand car batteries are sold with the claim that they will last for at least 4 years. Weibang, having boosted his car (with a 3.5-year-old Tudor battery) many times this past winter, believes that the mean battery life is less than four years. A random sample of eight batteries was taken. The batteries were operational for the following time periods (months): 40, 41, 52, 48, 44, 47, 45, 43. (s =3.9 months). At the 5% significance level, can Weibang support his claim that Tudor batteries last less than four years?

During the first quarter of 2015, Toronto Dominion Bank (TD) stock cost $45 per share, was expected to yield 4% per year in dividends, and had a risk index of 3.0 per share, while CNA Financial Corp. (CNA) stock cost $40 per share, was expected to yield 2.5% per year in dividends, and had a risk index of 2.0 per share.† You have up to $25,000 to invest in these stocks, and would like to earn at least $760 in dividends over the course of a year. (Assume the dividends to be unchanged for the year.) How many shares (to the nearest tenth of a unit) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio?

Toronto Dominion Bank__________ shares

CNA Financial Corp.___________ shares

What is the minimum total risk index? (Round your answer to two decimal places.)

Maximize p = x subject to

HINT [See Examples 1 and 2.]

Your company's new portable phone/music player/PDA/bottle washer, the RunMan, will compete against the established market leader, the iNod, in a saturated market. (Thus, for each device you sell, one fewer iNod is sold.) You are planning to launch the RunMan with a traveling road show, concentrating on two cities, New York and Boston. The makers of the iNod will do the same to try to maintain their sales. If, on a given day, you both go to New York, you will lose 500 units in sales to the iNod. If you both go to Boston, you will lose 250units in sales. On the other hand, if you go to New York and your competitor to Boston, you will gain 2,000 units in sales from them. If you go to Boston and they to New York, you will gain 1,000 units in sales. What percentage of time should you spend in New York and what percentage in Boston?

You should spend _________ of your time in New York and___________ in Boston.

How do you expect your sales to be affected?

The expected outcome is a net gain in RunMan sales.

The expected outcome is a net loss of RunMan sales.  

The expected outcome is no net gain or loss of RunMan sales.

Real Fruit Juice (Raw Data, Software Required):
A 32 ounce can of a popular fruit drink claims to contain 20% real fruit juice. Since this is a 32 ounce can, they are actually claiming that the can contains 6.4 ounces of real fruit juice. The consumer protection agency samples 30 such cans of this fruit drink. The amount of real fruit juice in each can is given in the table below. Test the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces. Test this claim at the 0.10 significance level.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 65 professional actors, it was found that 43 were extroverts.

(a)

Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b)

Find a 95% confidence interval for p. (Round your answers to two decimal places.)
lower limit          
upper limit         

Measuring the height of a California redwood tree is very difficult because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in Redwood represent the height ( in feet) and diameter ( in inches) at the breast height of a person for a sample of 21 California redwood trees.

a. Assuming a linear relationship, use the least- squares method to compute the regression coefficients b0 and b1. State the regression equation that predicts the height of a tree based on the tree’s diameter at breast height of a person.

b. Interpret the meaning of the slope in this equation.

c. Predict the mean height for a tree that has a breast height diameter of 25 inches.

d. Interpret the meaning of the coefficient of determination in this problem.

e. Perform a residual analysis of the results and determine the adequacy of the model.

f. Determine whether there is a significant relationship between the height of redwood trees and the breast height diameter at the 0.05 level of significance.

g. Construct a 95% confidence interval estimate of the population slope between the height of the redwood trees and breast height diameter.

h. What conclusion can you reach about the relationship between the diameter of the tree and its height?

A factory manufactures two kinds of ice​ skates: racing skates and figure skates. The racing skates require 6 ​work-hours in the fabrication​ department, whereas the figure skates require 5 ​work-hours there. The racing skates require 3 ​work-hours in the finishing​ department, whereas the figure skates require 3 ​work-hours there. The fabricating department has available at most 132 ​work-hours per​ day, and the finishing department has no more than 72 ​work-hours per day available. If the profit on each racing skate is $ 6 and the profit on each figure skate is $ 7 comma how many of each should be manufactured each day to maximize​ profit? ​ (Assume that all skates made are​ sold.) How many of each kind of skate should be manufactured each day to achieve maximum​ profit?
The factory should manufacure ____racing skates and _____figure skates each day.

MBA 6300 Case Study No. 2

There are numerous variables that are believed to be predictors of housing prices, including living area (square feet), number of bedrooms, and number of bathrooms. The data in the Case Study No. 2.xlsx file pertains to a random sample of houses located in a particular geographic area.

1. Develop the following simple linear regression models to predict the sale price of a house based upon a 90% level of confidence. Write the regression equation for each model.
   1. Sale price based upon square feet of living area.
   2. Sale price based upon number of bedrooms.
   3. Sale price based upon number of bathrooms.
2. Develop the following multiple linear regression models to predict the sale price of a house based upon a 90% level of confidence. Write the regression equation for each model.
   1. Sale price based upon square feet of living area and number of bedrooms.
   2. Sale price based upon square feet of living area and number of bathrooms.
   3. Sale price based upon number of bedrooms and number of bathrooms.
   4. Sale price based upon square feet of living area, number of bedrooms, and number of bathrooms.
3. Discuss the joint statistical significance of each of the preceding simple and multiple linear regression models at a 90% level of confidence and 95% level of confidence.
4. Discuss the individual statistical significance of the coefficient for each independent variable for each of the preceding simple and multiple linear regression models at a 90% level of confidence and 95% level of confidence.
5. Compare any of the preceding simple and multiple linear regression models that were found to be jointly and individually statistically significant at a 90% level of confidence and select the preferred regression model. Explain your selection using the appropriate regression statistics.
6. Interpret the coefficient for each independent variable (or variables) associated with your selected preferred regression model.
7. Using the preferred regression model, predict the sale price of a house with the following values for the independent variables: 3,000 square feet of living area, 3 bedrooms, and 2.5 bathrooms. (Hint: You should only use the values for those independent variables that are specifically associated with your selected preferred regression model.)

Prepare a single Microsoft Excel file using a separate worksheet for each question and upload your Excel file.

The system will not let me post all of the data needed to answer the question... it says that it is too long . could you save this information so i can add the data ?

Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.

A sample of 62 stocks traded on the NYSE that day showed that 27 went up.

You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of α=0.10α=0.10.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is more than 0.3.
• There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is more than 0.3.
• The sample data support the claim that the proportion of stocks that went up is is more than 0.3.
• There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.

In a recent Super Bowl, a TV network predicted that 87 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 44 people who saw the commercials and found that 39 of them said they would watch one of the television shows.

Suppose you are have the following null and alternative hypotheses for a test you are running:

H0:p=0.87H0:p=0.87
Ha:p≠0.87Ha:p≠0.87

Calculate the test statistic, rounded to 3 decimal places

z=z=

A researcher wants to know if calcium is an effective treatment for lowering blood pressure. He assigns one randomly chosen group of subjects to take calcium supplements; the other group will get a placebo. At the end of the treatment period, he measures the difference in blood pressure. The 50 members of the calcium group had blood pressure lowered by an average of 25 points with standard deviation 10 points. The 50 members of the placebo group had blood pressure lowered by an average of 15 points with standard deviation 8 points. Is there evidence that calcium is an effective treatment for lowering blood pressure? State your hypotheses, the test statistic and p-value, and then write a conclusion in terms of the problem. Please show solution using Ti-83 plus

5. People’s Choice, a monthly magazine, claimed that more than 40% of its subscribers had an annual income of $100,000 or more. In a random sample of 62 subscribers, 30 had incomes of $100,000 or more. Using a significance level of 0.10, does this information substantiate the claim of the magazine? Show all test parts to receive full credit. (15 pts)