1. Assume the branch manager is not satisfied with the widths of the obtained confidence intervals, and she requests estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of No Gulf View condominiums with a margin of error of $15,000. Using 95% confidence, how should the sample sizes be?

   Gulf View Condominiums		No Gulf View Condominiums
   List Price	Sale Price	List Price	Sale Price
   495.0	475.0	227.0	227.0
   379.0	350.0	158.0	145.5
   529.0	519.0	196.5	189.0
   552.5	534.5	249.0	240.0
   334.9	334.9	289.0	277.5
   550.0	505.0	225.0	224.0
   169.9	165.0	289.0	269.0
   210.0	210.0	189.9	186.5
   975.0	945.0	159.9	154.9
   314.0	314.0	245.0	240.0
   315.0	305.0	209.8	202.0
   885.0	800.0	220.0	205.0
   975.0	975.0	236.0	222.0
   469.0	445.0	159.9	156.5
   329.0	305.0	170.0	170.0
   365.0	330.0	332.0	302.5
   332.0	312.0	197.5	189.0
   520.0	495.0	257.0	237.0
   425.0	405.0
   675.0	669.0
   409.0	400.0
   649.0	649.0
   319.0	305.0
   425.0	410.0
   359.0	340.0
   469.0	449.0
   895.0	875.0
   439.0	430.0
   435.0	400.0
   235.0	227.0
   638.0	618.0
   629.0	600.0
   329.0	309.0
   595.0	555.0
   339.0	315.0
   215.0	200.0
   395.0	375.0
   449.0	425.0
   499.0	465.0
   439.0	428.5

You may need to use the appropriate appendix table or technology to answer this question. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 32 years of rainfall for California and a sample of 48 years of rainfall for New York has been taken.

b.What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)

c.What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)

d.In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?

Define each of them and show the process of solving them with Excel.

What is critical value/standardized test statistic z/standardized test statistic t/P-value?

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.

If p is any positive number between 0 and 1, then p4 + C(4,3) p3(1–p) + C(4,2) p2(1–p)2 + C(4,1) p (1–p)3 + (1–p)4 = 1. Explain why without performing any calculation.

Please explain the concept behind this to me, and not just the chain of calculations or mathematical proofs.

Six hundred and five survivors of a heart attack, were randomly assigned to follow either (1) a diet close to the "prudent diet step 1" of the American Heart Association or (2) a Mediterranean-type diet consisting of more bread and cereals, more fresh fruit and vegetables, more grains, more fish, fewer delicatessen food, less meat. Over four years, researchers collected information on number of deaths from cardiovascular causes e.g., heart attack and strokes. Of the 303 survivors who followed the AHA diet 24 died of cardiovascular disease. Of the 302 survivors who followed the Mediterranean diet, 14 died of cardiovascular disease. Is there a significant difference in the proportion of patients who die of cardiovascular disease across the two diet plans? Run the test at a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUSTshow your work to receive full credit. Partial credit is available.

As you read about regression this week, try to think of pairs of variables whose values might be associated, or as we say in statistics have a correlation. For example, height and weight have a positive correlation because in general we expect taller people to weigh more than shorter people. This does not mean every taller person weighs more than every shorter person, but that's the tendency. Can you think of another pair of variable that have a positive correlation? How about a pair of variables that have a negative correlation? Try to think of pairs of variables from your field of study! For each variable, consider the following: give a brief description of each variable, how is it measured, what are its possible values, Why do you think the correlation between your two variables is positive or negative?

The following frequency distribution shows the price per share for a sample of 30 companies listed on the New York Stock Exchange.

Compute the sample mean price per share and the sample standard deviation of the price per share for the New York Stock Exchange companies (to 2 decimals). Assume there are no price per shares between 29 and 30, 39 and 40, etc.

Q 4
A computer program translates texts between different languages. Experience shows that the probability of a word being incorrectly translated is 0.002.
We enter a text with 5000 words.
What is the probability that no word is translated incorrectly? (Tips, Po)
What is the probability that at most 2 words will be translated incorrectly?
What is the probability that 3 or more words are translated incorrectly?

The better-selling candies are often high in calories. Assume that the following data show the calorie content from samples of M&M's, Kit Kat, and Milky Way candies.

Test for significant differences among the calorie content of these three candies.

A) State the null and alternative hypotheses.

H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM ≠ Median_KK ≠ Median_MW

H₀: All populations of calories are identical.
H_a: Not all populations of calories are identical.    

H₀: Not all populations of calories are identical.
H_a: All populations of calories are identical.

H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM > Median_KK > Median_MW

H₀: Median_MM ≠ Median_KK ≠ Median_MW
H_a: Median_MM = Median_KK = Median_MW

B) Find the value of the test statistic. (Round your answer to two decimal places.)

C) Find the p-value. (Round your answer to three decimal places.)

D) At a 0.05 level of significance, what is your conclusion?

Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.    

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

What are the major difference between univariate, bivariate, and multivariate analysis?

What is the difference between correlation and regression?

Inferential statistics allow us to

Consider the random experiment of tossing two fair dice and recording the up faces. Let X be the sum of the two dice, and let Y be the absolute value of the difference of the two dice.

1.Compute the skewness coefficient and kurtosis of the distribution of X and Y.

2. For each of x=4,5,6 from the sample space of X do the following:

Construct the pff of the conditional distribution of X given Y = y

Compute the mean variance SD skewness coefficient snd kurtosis of the conditional distribution of Y given X = x. Are they distributional characteristics constant, or do they depend upon x?

Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $35 per passenger. Suppose a random sample of 80 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $38. Use z-table.

b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?

c. What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?

A qualifying exam for a graduate school program has a math section and a verbal section. Students receive a score of 1, 2, or 3 on each section. Define X as a student’s score on the math section and Y as a student’s score on the verbal section. Test scores vary according to the following bivariate probability distribution.

μXX =   , and μYY =   

σXX =   , and σYY =   

The covariance of X and Y is ________ . The coefficient of correlation is _________ . The variables X and Y_______ independent.

The expected value of X + Y is_______ , and the variance of X + Y is ________________ .

To be accepted to a particular graduate school program, a student must have a combined score of 4 on the qualifying exam.

What is the probability that a randomly selected exam taker qualifies for the program?

0.46

0.33

0.47

0.45

Chebysheff’s Theorem states that the proportion of observations in any population that lie within k standard deviations of the mean is at least 1 – 1 / k² (for k > 1).

According to Chebysheff’s Theorem, there is at least a 0.75 probability that a randomly selected exam taker has a combined score between_______ and_______ .