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_______ .

Problem 4: House Prices

Use the “Fairfax City Home Sales” dataset for parts of this problem.

a) Use StatCrunch to construct an appropriately titled and labeled relative frequency histogram of Fairfax home closing prices stored in the “Price” variable. Copy your histogram into your document.

b) What is the shape of this distribution? Answer this question in one complete sentence.

c) Assuming the population has a similar shape as the sample with population mean $510,000 and population standard deviation $145,000; calculate the probability that in a random sample of size 10, the mean of the sample will be greater than $600,000. You may assume a random sample was taken and the sample came from a big population. However, be sure to check the central limit theorem condition of a large sample size before completing this problem using one complete sentence. If this condition is not met, you cannot complete the problem.

d) Assuming the population has a similar shape as the sample with population mean $510,000 and population standard deviation $145,000; calculate the probability that in a random sample of size 36, the mean of the sample will be greater than $600,000. You may assume a random sample was taken and the sample came from a big population. However, be sure to check the central limit theorem condition of a large sample size before completing this problem using one complete sentence. If this condition is not met, you cannot complete the problem.

Data:

Price Year, Days, TLArea, Acres

369900   1922   44   1870   0.39

373000   1952   0   1242   0.27

375000   1952   8   932   0.15

375000   1950   2   768   0.19

379000   1952   31   816   0.21

380000   1941   53   1092   0.19

385000   1951   5   984   0.27

387700   1953   5   975   0.36

395000   1954   18   957   0.29

395000   1951   12   1105   0.22

399900   1954   29   1206   0.28

399900   1951   6   1226   0.18

400000   1954   31   957   0.27

410000   1949   6   1440   0.2

410000   1954   17   1344   0.23

412500   1954   4   1008   0.25

415000   1953   17   1371   0.28

420000   1954   2   957   0.25

426000   1952   3   1694   0.25

430000   1953   19   975   0.23

434900   1950   5   1128   0.18

435000   1954   32   1252   0.24

440000   1960   3   1161   0.26

440000   1954   2   1036   0.28

440000   1955   12   1645   0.28

440000   1960   5   1746   0.31

441000   1952   133   1062   0.23

442000   1961   4   1414   0.32

443000   1951   26   962   0.2

444900   1955   4   1122   0.19

446500   1953   3   962   0.26

450000   1952   2   1488   0.15

450000   1955   49   1122   0.23

450000   1979   0   1092   0.28

450000   1951   70   962   0.2

450000   1957   23   1300   0.51

451000   1947   12   1325   0.34

455000   1952   7   2267   0.81

455000   1962   4   1050   0.31

460000   1955   5   997   0.3

460000   1954   10   1125   0.17

465000   1954   77   1288   0.46

465900   1947   21   1309   0.19

469000   1963   153   1149   0.27

474000   1959   5   1319   0.32

475000   1955   4   1530   0.28

475000   1953   29   1008   0.2

475000   1955   6   1530   0.28

475000   1956   116   1345   0.5

475000   1956   1   1530   0.28

480000   1960   27   1236   0.27

480000   1959   133   1527   0.24

485000   1955   4   1008   0.24

485000   1956   74   977   0.24

488000   1960   11   1972   0.33

500000   1963   0   2145   0.25

500000   1953   14   1758   0.54

500500   1955   6   1630   0.28

510000   1959   5   1680   0.34

512000   1963   0   1968   0.22

519000   1961   1   1312   0.29

520000   1954   15   1492   0.25

520000   1958   80   1443   0.33

520000   1963   122   1822   0.32

530000   1962   6   1393   0.29

540000   1962   12   1414   0.25

543600   1962   4   1414   0.24

560000   1967   5   1530   0.28

560000   1961   16   1438   0.53

565000   1947   6   1510   0.25

565500   1967   5   1217   0.26

589000   1954   32   2368   0.3

593000   1954   9   2044   0.25

610000   1978   140   2091   0.09

655000   1976   180   2728   0.24

660000   1947   10   2635   0.22

665000   1950   37   2645   0.57

685000   1982   120   2752   0.09

795000   2002   259   3402   0.12

852000   2000   4   3215   0.11

895000   2000   63   3230   0.11

930000   2015   135   3175   0.15

940000   1860   42   3038   0.57

968500   1850   74   3630   0.34

1100000   2004   161   3640   0.19

The probability of success is 0.68. A sample of 15 is taken. Assume independent trials. (Please show your work here)

1. What is the probability of succeeding all 15 times?

2. What is the probability of succeeding 9 times in 15 trials?

3. What is the probability of succeeding 14 times in 15 trials?

4. What is the probability of succeeding 12 or more times in 15 trials?

5. What is the probability of succeeding 11 or fewer times in 15 trials?

PLEASE SOLVE ALL PARTS AND EXPLAIN IN DETAIL.

I'M HAVING A DIFFICULT TIME UNDERSTANDING HOW TO FIND/SOLVE THESE TYPES OF PROBLEMS:

In 2017, as reported by ACT Research Service, the mean ACT Math score was μ=20.6 μ=20.6 . ACT Math scores are normally distributed with σ=4.8 σ=4.8 .

1. What is the probability that a randomly selected test taker has an ACT Math score less than 18? Is this result unusual? Explain.
2. Describe the sampling distribution of x ˆ  x^ , the sample mean ACT Math score for a random sample of 40 tests using the N(mean, standard deviation) notation.
3. What is the probability that a random sample of 40 tests has a mean ACT Math score less than 18? Is this result unusual? Explain.
4. What is the difference in part a and c in this question?

Develop a branding strategy for your credit repair service service that covers the brand name, logo, slogan, and at least one brand extension.

A 95% confidence interval for the average waiting time at the drive-thru of a fast food restaurant if a sample of 192 customers have an average waiting time of 92 seconds with a population deviation of 23 seconds

round to the nearest hundredth of a second

Question 1

Given a normal distribution with µ =15 and σ =5, what is the probability that

1. 5% of the values are less than what X values?
2. Between what two X values (symmetrically distributed around the mean) are 95 % of the values?

INSTRUCTIONS: Show all your work as to how you have reached your answer. Please don’t simply state the results. Show graphs where necessary.

Use the sample information x¯ = 36, σ = 7, n = 17 to calculate the following confidence intervals for μ assuming the sample is from a normal population.

(a) 90 percent confidence. (Round your answers to 4 decimal places.) The 90% confidence interval is from to

(b) 95 percent confidence. (Round your answers to 4 decimal places.) The 95% confidence interval is from to

(c) 99 percent confidence. (Round your answers to 4 decimal places.) The 99% confidence interval is from to

(d) Describe how the intervals change as you increase the confidence level.