The heights of South African men are normally distributed with a mean of 69 inches and a standard deviation of 4 inches. What is the probability that a randomly selected South African man is taller than 72 inches (sample size of 1)?   What is the probability that a sample of 100 has a mean greater than 72 inches?

In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.)

(a)    Φ(c) = 0.9854


(b)    P(0 ≤ Z ≤ c) = 0.3078


(c)    P(c ≤ Z) = 0.1210


(d)    P(−c ≤ Z ≤ c) = 0.6680


(e)    P(c ≤ |Z|) = 0.0160

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Using data from 50 workers, a researcher estimates Wage = β0 + β1 Education + β2 Experience +β3 Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. Coefficients Standard Error t Stat p-value Intercept 7.42 4.14 1.40 0.0524 Education 1.53 0.39 3.65 0.0002 Experience 0.47 0.20 3.53 0.0026 Age −0.07 0.08 −0.19 0.8130 a-1. What is the point estimate for β1? 1.53 0.47 a-2. Interpret this value. As Education increases by 1 unit, Wage is predicted to increase by 1.53 units, holding Age and Experience constant. Same interpretation by using 0.47 or -0.07 a-3. What is the point estimate for β2? 0.47 1.53 a-4. Interpret this value. Same interpretation by using 1.53 or -0.07 As Experience increases by 1 unit, Wage is predicted to increase by 0.47 units, holding Age and Education constant. b. What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.) y-hat = + Education + Experience + Age c. What is the predicted value for Age = 40, Education = 4 and Experience = 3. (Do not round intermediate calculations. Round your answer to 2 decimal places.) y-hat

NEEDS TO BE SOLVED WITH A TEMPLATE FOR HYPOTHESIS TESTING IN EXCEL

A company can choose between two brands of light bulbs for an office complex and wants to know if one brand lasts longer than another brand. Test results for the two brands are shown in the table below. Is there persuasive evidence for company officials to conclude at α = 0.05 that there is a difference in the length of life of the lightbulbs?

“Learn to Write A Great Country Song” has become the top selling book and Shania wanted to know whether the book worked better for one gender. So Shania asked 10 males and 15 females to spend 14 hours over a week period to write a song using the book. All songs were subsequently ranked, and the sum of ranks for males equaled 77 while the sum of ranks for females equaled 248. Use a Mann-Whitney U test.

In the box below, provide the following information:

Null Hypothesis in sentence form (1 point):

Alternative Hypothesis in sentence form (1 point):  
Critical Value(s) (2 points):

Calculations (4 points): Note: the more detail you provide, the more partial credit that I can give you if you make a mistake.

Outcome (determination of significance or not, effect size if appropriate, and what this reflects in everyday language, 2 points)

Which of the following correlation values represents the strongest linear relationship between two quantitative variables?

A plan for an executive travelers’ club has been developed by airline on the premise that 5% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who would qualify.   

1. Write down the null and alternative hypotheses.

2. Explain whether this is a one-sided or a two-sided test, and why.

3. What is the value of the test statistic for your observed results?

4. What is the p-value for your observed results?

5. What is your conclusion? Please use words that a non-statistics student would understand, and justify your answer. Assume a significance level of .05.

6. Based on your conclusion, what type of error are you risk at?

A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.05 years, with sample standard deviation s = 0.88 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 1.75 yr; H₁: μ < 1.75 yr

H₀: μ < 1.75 yr; H₁: μ = 1.75 yr    

H₀: μ > 1.75 yr; H₁: μ = 1.75 yr

H₀: μ = 1.75 yr; H₁: μ ≠ 1.75 yr

H₀: μ = 1.75 yr; H₁: μ > 1.75 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is known.

The Student's t, since the sample size is large and σ is known.    

The Student's t, since the sample size is large and σ is unknown.

The standard normal, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Find the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.

There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.  

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 49% of all such batches contain no defective components, 33% contain one defective component, and 18% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.

no defective components=?

one defective component=?

two defective components=?

(b) One of the two tested components is defective. [Hint: Draw a tree diagram with three first-generation branches for the three different types of batches.]

no defective components=?

one defective component=?

two defective components=?

A company operates a solar installation in the desert in Western Australia. It is reviewing its operating practices with a view to making them more efficient. The solar installation generates electric power from sunlight and incurs operating costs for cleaning the solar modules (sometimes called solar panels) and replacing solar modules that have failed.

a) The annual revenue from the electric power is variable due to variable cloudiness and solar module failure and has a mean of $2.78m and a standard deviation of $0.32m. The annual operating costs have a mean of $0.51m and a standard deviation of $0.12m. Expected revenue varies systematically from one month to another, being higher in the summer when there is more sunshine. Monthly operating costs follow the same probability model regardless of the month (same mean and standard deviation apply to all months). Calculate, if possible, the mean and standard deviation of (i) monthly operating costs (ii) monthly profits. If a calculation is not possible, give the reason.

Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as

follows for the past 12 weeks:

WEEK ACTUAL PASSENGER MILES (1,000S)

1            17

2            21

3            19

4            23

5            18

6            16

7            20

8            18

9            22

10         20

11         15

12         22

Assuming an initial forecast for week 1 of 17,000 miles, use exponential smoothing to

compute miles for weeks 2 through 12. Use α = 0.2.

What is the MAD for this model?

Compute the RSFE and tracking signals. Are they within acceptable limits?

PLEASE ANSWER THE RSFE question Thank you

A school administrator is interested in a schools performance in math.  He administers a math test to a sample of 30 students and obtains a mean of 84.25.  The standard deviation of this sample was 8.4. (T Test)

26. Construct a 95% confidence interval for this data.

27. How would you interpret this confidence interval?

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 9. The hypotheses H₀: μ = 75 and H_a: μ < 75 are to be tested using a random sample of n = 25 observations.

(a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.)
standard deviations

(b) If x = 72.3, what is the conclusion using α = 0.002?
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75.Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75.    Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75.Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75.

(c) For the test procedure with α = 0.002, what is β(70)? (Round your answer to four decimal places.)
β(70) =

(d) If the test procedure with α = 0.002 is used, what n is necessary to ensure that β(70) = 0.01? (Round your answer up to the next whole number.)
n =  specimens

(e) If a level 0.01 test is used with n = 100, what is the probability of a type I error when μ = 76? (Round your answer to four decimal places.)

2. (Binomial model) Consider a roulette wheel with 38 slots, of which 18 are red, 18 are black, and 2 are green (0 and 00). You spin the wheel 6 times.

(a) What is the probability that 2 of those times the ball ends up in a green slot? (

b) What is the probability that 4 of those times the ball ends up in a red slot?

3. (Normal approximation to binomial model) Take the roulette wheel from question 2. Assume that the wheel is spun 100 times, and you are interested in whether the ball ends up in a red slot.

(a) Verify that you can use the normal model here.

(b) Find the probability that the ball ends up in a red slot at least 60 times.

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week.

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
4. Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.01 significance level.
5. Estimate the p-value.