Random sample of size n=19 is taken from a Normal population, sample mean is 11.5895, standard deviation is 1.0883.

1. At the 2% level, test whether it is reasonable to believe that the true population variance is larger than 1.

Using the scenario from above, do the following

2. Derive the power function. Show your work.
3. Using R, graph the power function for 0.5 < sigma^2 < 3.5.
4. Pretend that the sample size was actually 56. Plot this power function on the same graph.
5. Based on the power functions graphed in c, why is the test described in part c "better" than the original test? Explain your answer using the power functions.

For PART B USE A TI 84 AND LIST THE STEPS THAT YOU DID! THANK YOU

Researchers want to determine whether all bags of Skittles® have the same proportion of colors regardless of the flavor of Skittles®. To test this, they randomly sampled king-size bags of each flavor and recorded their findings in the table.

Part A: What are the correct degrees of freedom for this table? (2 points)

Part B: Calculate the expected count for the number of blue tropical Skittles®. Show your work. (3 points)

Part C: Is there sufficient evidence that there is a difference in the proportion of colors for the different flavors of Skittles®? Provide a statistical justification for your conclusion. (5 points)

The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket. Airfares were based on the total ticket value, which consisted of the price charges by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $120. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $555 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $250 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $470 (to 4 decimals)?

d. What is the cost for the 4% highest domestic airfares? [(round to nearest dollar) (more or less)]

2) A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were:

3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

-Assuming a normal population, use Minitab to construct a 95 percent confidence interval for the true mean weight. You will need to enter the data. Attach or include your output. (4 points)

-Write a sentence using the confidence interval found in part a. (3 points)

-Use Minitab to construct a histogram of the sample data. Use the histogram to determine if the

assumption of normality is a valid assumption. State your findings. (4 points)

-What sample size would be necessary to estimate the true weight with an error of ± 0.025 gram

with 90 percent confidence? (4 points)

Explain the differences between a sample and a population, and offer example (s) to further illustrate your explanation

Answer the following questions and use Excel or this document to show your work.

1. Consider the following results for two samples randomly taken from two normal populations with equal variances.

a. Develop a 95% confidence interval for the difference between the two population means.

b. Is there conclusive evidence that one population has a larger mean? Explain.

2. Explain why depression is a hypothetical construct instead of a concrete variable. Describe how depression might be measured and defined using an operational definition. TIP: The more details you provide for the operational definition the better your mark. It should be your OWN definition not a psychological test used already. Doing some research on what are clinical indicators for depression will help you better answer this question. (6 points)

A supermarket chain analyzed data on sales of a particular brand of snack cracker

at 104 stores for a certain one week period. The analyst decided to build a regresion model to predict the sales of the snack cracker based on the total sales of all brands in the snack cracker category.

f. Produce a 90% confidence prediction interval for the sales of the cracker

   in a store where the category sales is 1005. Also produce the90 %

   confidence prediction interval in a store where category sales is 900.

  Can you with 90% confidence claim which store has higher cracker sales?

Use the data given in the table to answer the following questions. The data represents the average number of miles that a salesperson travels in a day verses the number of sales made each month.

(a) What is the value of the correlation coefficient for this set of data? Round to 3 decimal places.

(b) What is the equation of the Regression Line for this set of data? Round values to two decimal places.

(c) Predict the number of sales an associate could expect to make if he travelled an average of 108 miles each day. Round to two decimal places.

Corporate advertising tries to enhance the image of the corporation. A study compared two ads from two sources, the Wall Street Journal and the National Enquirer. Subjects were asked to pretend that their company was considering a major investment in Performax, the fictitious sportswear firm in the ads. Each subject was asked to respond to the question "How trustworthy was the source in the sportswear company ad for Performax?" on a 7-point scale. Higher values indicated more trustworthiness. Here is a summary of the results. Ad source n x s Wall Street Journal 66 4.77 1.50 National Enquirer 61 2.43 1.64 Find the two-sample pooled t statistic. Then formulate the problem as an ANOVA and report the results of this analysis. Verify that F = t 2.

1.13. Problem. (Section 3.4) Three black boxes are labeled with Roman numerals I, II and III. • Box I contains four red chips and three blue chips. • Box II contains two red chips and five blue chips. • Box III contains seven red chips and no blue chips. Solve each of the following problems.

(a) Suppose a box is selected at random and three chips are drawn at random from the box. If all three chips are red, what is the probability they were drawn from Box I?

(b) Suppose one chip is selected at random from each box. If two of the three chips drawn are red chips, what is the probability that the chip drawn from Box II was red?

(c) Suppose three chips are randomly selected from Box I and placed in Box III. If a chip subsequently drawn randomly from Box III is blue, what is the probability that all three chips moved from Box I to Box III were blue.

Evaluate the differences between dependent and independent samples. Would our random samples need to come from the same "overall" population?

1.14. Problem. (Section 3.4) A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and, of these 312 men, 102 died from causes related to heart disease. Determine the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease. Upon arrival at a hospital’s emergency room, patients are categorized according to their condition as critical, serious, or stable. In the past year,

• 10% of ER patients were critical

• 30% of ER patients were serious

• 60% of ER patients were stable

• 40% of critical patients died.

• 10% of the serious patient died.

• 1% of the stable patients died. Given a patient survived, what is the probability that they were categorized as serious upon arrival?

1.11. Problem. (Sections 2.2-2.4, 3.1) Five cards are drawn from a standard deck of 52 cards.

(a) Given that exactly three of the five cards show a hearts suit, calculate the probability that the hand also includes a three-of-a-kind.

(b) Given that the five card hand contains a three-of-kind, find the probability that it contains at three hearts.