26% of all college students major in STEM (Science, Technology, Engineering, and Math). If 44 college students are randomly selected, find the probability that a. Exactly 9 of them major in STEM. Incorrect b. At most 14 of them major in STEM. Incorrect c. At least 9 of them major in STEM. Incorrect d. Between 7 and 13 (including 7 and 13) of them major in STEM.

Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed.

51

34 

59

52 

27

27

51  

34

59

31  

52

51

41

​(a) Find the sample mean and sample standard deviation.

​(b) Each employee in the sample is given a

66​%

raise. Find the sample mean and sample standard deviation for the revised data set.

​(c) To calculate the monthly​ salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set.

​(d) What can you conclude from the results of​ (a), (b), and​ (c)

According to a social media​ blog, time spent on a certain social networking website has a mean of 19 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 44 minutes. Complete parts​ (a) through​ (d) below

a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 18.5 and 19.5 ​minutes?

b. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 18 and 19 ​minutes?

c. If you select a random sample of 100 ​sessions, what is the probability that the sample mean is between 18.5 and 19.5 ​minutes?

Explain the difference in the results of​ (a) and​ (c).

c. The sample size in​ (c) is greater than the sample size in​ (a), so the standard error of the mean​ (or the standard deviation of the sampling​ distribution) in​ (c) is

less or greater than in​ (a). As the standard error decreases/increases values become more concentrated around the mean.​ Therefore, the probability that the sample mean will fall in a region that includes the population mean will always decrease/increase when the sample size increases.

A store has N clients per day, where the probability that N will be three is 0.1, that N will be two is 0.4, that N will be one is 0.3. The store never gets more than three clients per day.

(a) Is N binomial? Poisson?

(b) Write the cumulative distribution function for N.

(c) What is the average number of clients per day?

(d) You want to study how many bags of milk each client buys. Half of them buy two bags, a quarter buy 1 bag, and the rest buy none. Let X be the number of bags of milk purchased on a given day. Are X and N independent?

(e) What is the probability that 5 bags will be purchased?

(f) What is the probability that there will be 3 clients and that 5 bags will be purchased?

(g) What is the probability the 5 bags will be purchased given that there are three clients?

(h) Find the probability function of X.

As the production manager of the Neptune Boat Corporation, you must determine how many units of the Model 4W speedboat to produce over the next four quarters. The company has a starting inventory of 75 units, and demand is 125 units in quarter 1, 100 units in quarter 2, 40 units in quarter 3, and 20 units in quarter 4. Production capacity is limited to 70 units in quarter 1, 90 units in quarter 2, 50 units in quarter 3, and 60 units in quarter 4. The inventory cost during quarters 1 and 2 is $200 per unit per quarter, and $300 per unit per quarter during quarters 3 and 4. Production costs for the first quarter are $8,000 per unit, and these costs increase by 10% per quarter due to increasing labor and material costs. Neptune’s senior management has indicated that the ending inventory for quarter 4 must be at least 30 units. Develop a linear programming model that Neptune can use to determine the optimal production schedule that will minimize the total cost of meeting demand for the Model 4W speedboat in each quarter, subject to the capacity and inventory constraints. You do not need to solve the LP.

Jobs and productivity! How do banks rate? One way to answer this question is to examine annual profits per employee. The following is data about annual profits per employee (in units of 1 thousand dollars per employee) for representative companies in financial services. Assume σ ≈ 9.3 thousand dollars.

(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
thousand dollars

(b) Let us say that the preceding data are representative of the entire sector of (successful) financial services corporations. Find a 75% confidence interval for μ, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)

(c) Let us say that you are the manager of a local bank with a large number of employees. Suppose the annual profits per employee are less than 30 thousand dollars per employee. Do you think this might be somewhat low compared with other successful financial institutions? Explain by referring to the confidence interval you computed in part (b).

Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions.Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.     No. This confidence interval suggests that the bank profits are less than those of other financial institutions.No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

(d) Suppose the annual profits are more than 40 thousand dollars per employee. As manager of the bank, would you feel somewhat better? Explain by referring to the confidence interval you computed in part (b).

No. This confidence interval suggests that the bank profits are higher than those of other financial institutions.No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.     Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions.Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

(e) Find a 90% confidence interval for μ, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)

(f) Let us say that you are the manager of a local bank with a large number of employees. Suppose the annual profits per employee are less than 30 thousand dollars per employee. Do you think this might be somewhat low compared with other successful financial institutions? Explain by referring to the confidence interval you computed in part (e).

Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions.Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.     No. This confidence interval suggests that the bank profits are less than those of other financial institutions.No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

(g) Suppose the annual profits are more than 40 thousand dollars per employee. As manager of the bank, would you feel somewhat better? Explain by referring to the confidence interval you computed in part (e).

No. This confidence interval suggests that the bank profits are higher than those of other financial institutions.No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.     Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions.Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

Researchers at a food company are interested in how a new spaghetti sauce made from green tomatoes (and green in color) will compare to its traditional red spaghetti sauce. The company is worried that the green color will adversely affect the tastiness scores. It randomly assigns subjects to either the green or red sauce condition. Subjects indicate the tastiness of the sauce on a 10-point scale. Tastiness scores tend to be skewed. The scores follow:

RS GS

7 | 4

6 | 5

9 | 6

10 | 8

6 | 7

7 | 6

8 | 9

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

QUESTION
Two types of medication for hives are being tested. The manufacturer claims that the new medication B is more effective than the standard medication A and undertakes a comparison to determine if medication B produces relief for a higher proportion of adult patients within a 30-minute time window. 20 out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. 12 out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. The hypothesis test is to be carried out at a 1% level of significance.

a. State the null and alternative hypotheses in words and in statistical symbols. (3 points)

b. What statistical test is appropriate to use? Explain the rationale for your answer. (3 points)

c. Would the test be right-tailed, left-tailed or two-tailed? Explain the rationale for your answer. (3 points)

d. Describe an outcome that would result in a Type I error. Explain the rationale for your answer. (3 points)

e. Describe an outcome that would result in a Type II error. Explain the rationale for your answer. (3 points)

To determine if their 2.50 inch steel handles are properly adjusted, Kane Manufacturing has decided to use an x‾x‾-Chart which uses the range to estimate the variability in the sample.

Step 1 of 7:

What is the Center Line of the control chart? Round your answer to three decimal places.

Step 2 of 7:

What is the Upper Control Limit? Round your answer to three decimal places.

Step 3 of 7:

What is the Lower Control Limit? Round your answer to three decimal places.

Step 4 of 7:

Use the following sample data, taken from the next time period, to determine if the process is "In Control" or "Out of Control".
Observations: 2.52,2.53,2.44,2.52,2.5,2.46
Sample Mean: 2.495

Step 5 of 7:

Use the following sample data, taken from the next time period, to determine if the process is "In Control" or "Out of Control".
Observations: 2.46,2.53,2.5,2.5,2.5,2.53
Sample Mean: 2.5033

Step 6 of 7:

Use the following sample data, taken from the next time period, to determine if the process is "In Control" or "Out of Control".
Observations: 2.56,2.48,2.58,2.59,2.55,2.56
Sample Mean: 2.5533

Step 7 of 7:

Based on the control limits established, what is the probability that the production manager will conclude that the process is "Out of Control", when the process is actually "In Control"? Round your answer to three decimal places.

**NO HANDWRITTEN ANSWERS PLEASE **

An automatic cookie machine at ACM, Inc. must deposit a specified amount of 25 0.3 grams (g) of dough for each cookie on a conveyor belt. It costs $0.03 to scrap a defective cookie. A sample of 50 cookies was drawn from the production process, which has been determined to be approximately normally distributed, and the results, in grams, can be found in worksheet tab Prob. 7-12 in the Excel file C07Data. a. What is the value of k in the Taguchi loss function? b. Determine how much the process varies from the target specification, based on the mean difference and standard deviation of the sample results. What is the expected loss per unit?

Question 10 (1 point)

You are looking for a way to incentivize the sales reps that you are in charge of. You design an incentive plan as a way to help increase in their sales. To evaluate this innovative plan, you take a random sample of your reps, and their weekly incomes before and after the plan were recorded. You calculate the difference in income as (after incentive plan - before incentive plan). You perform a paired samples t-test with the following hypotheses: Null Hypothesis: μ_D ≤ 0, Alternative Hypothesis: μ_D > 0. You calculate a p-value of 0.3076. What is the appropriate conclusion of your test?

Question 10 options:

Question 11 (1 point)

You are looking for a way to incentivize the sales reps that you are in charge of. You design an incentive plan as a way to help increase in their sales. To evaluate this innovative plan, you take a random sample of your reps, and their weekly incomes before and after the plan were recorded. You calculate the difference in income as (after incentive plan - before incentive plan). You perform a paired samples t-test with the following hypotheses: Null Hypothesis: μ_D ≤ 0, Alternative Hypothesis: μ_D > 0. You calculate a p-value of 0.0474. What is the appropriate conclusion of your test?

Question 11 options:

Question 12 (1 point)

Consumers Energy states that the average electric bill across the state is $62.74. You want to test the claim that the average bill amount is actually less than $62.74. The hypotheses for this situation are as follows: Null Hypothesis: μ ≥ 62.74, Alternative Hypothesis: μ < 62.74. If the true statewide average bill is $51.97 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Question 12 options:

Question 13 (1 point)

Consumers Energy states that the average electric bill across the state is $57.42. You want to test the claim that the average bill amount is actually greater than $57.42. The hypotheses for this situation are as follows: Null Hypothesis: μ ≤ 57.42, Alternative Hypothesis: μ > 57.42. If the true statewide average bill is $24.71 and the null hypothesis is rejected, did a type I, type II, or no error occur?

Question 13 options:

1. At a Midwestern University the 386 students in the Business School were classified according to their major within the business school and their gender. The results follow.

1. Find the probability that the selected student is a finance major and a male.

b. Find the probability that the selected student is an administration major or a finance major.

c. Find the probability that the selected student is an administration major or a female.

d. Find the probability that the selected student is finance major, given he is a male.

The data in the table show the number of pounds of bananas sold per week at a grocery store when the banana display was positioned in the produce, milk, and cereal sections of the store.

a) Perform a one-way ANOVA using

alphaαequals=0.05

to determine if there is a difference in the average number of pounds of bananas sold per week in these three locations.

b) If warranted, perform a multiple comparison test to determine which pairs are different using

alphaαequals=0.050

Pounds of Bananas Sold

Complete the ANOVA summary table below.

Please help, I am very confused

4.Assume that it is true that people can not tell the difference between Coke and Pepsi. If a sample of 15 people participated in a blind taste test, can we assume that the sampling distribution of the proportion of people that correctly chose Pepsi is normal?

Select one:

a. Yes

b. No

5.Consider the information in Question 4. What is the smallest possible sample size (i.e., number of people taking the blind taste test) needed to insure that the sampling distribution of the proportion is normal?

Select one:

a. 8

b. 10

c. 12

d. 18

e. 20