Scenario 4

A warehouse has a new leadership team and they wanted to prove their performance was as good or better than the previous leadership team. They measured on-time shipping and accurate order fulfillment. Their data showed a correlation value of 0.70 and a regression value of 0.49 between on-time shipping and accurate order fulfillment. The previous leadership teams’ corresponding numbers for on-time shipping and accurate order fulfillment were a correlation value of 0.80 and a regression value of 0.64.

1. What conclusions can you summarize from these numbers in plain English?

2. Based on this data what future course of action do you recommend for your client?

Scenario 5

The same warehouse leadership team in Scenario 4 measured damaged products and warehouse capacity. Their data showed a correlation value of -0.50 and a regression value of 0.25 between damaged products and warehouse capacity.

1. What conclusions can you summarize from these numbers in plain English?

2. Based on this data what future course of action do you recommend for your client?

4. Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table)

a. Construct the 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Confidence interval is to .

b. Specify the competing hypotheses in order to determine whether or not the population means differ.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

c. Using the confidence interval from part a, can you reject the null hypothesis?

• Yes, since the confidence interval includes the hypothesized value of 0.

• No, since the confidence interval includes the hypothesized value of 0.

• Yes, since the confidence interval does not include the hypothesized value of 0.

• No, since the confidence interval does not include the hypothesized value of 0.

d. Interpret the results at αα = 0.05.

• We conclude that population mean 1 is greater than population mean 2.

• We cannot conclude that population mean 1 is greater than population mean 2.

• We conclude that the population means differ.

• We cannot conclude that the population means differ.

Please explain how the proportions for two populations are used in hypotheses testing about two population proportions. Please give an example.

A simple random sample was taken of 1000 shoppers Respondents were classified by gender (male or female) and by meat department preference (beef, chicken, fish). Results are shown in the contingency table:

Is there a difference in meat preference between males and females? The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. Use a 0.05 level of significance.  

Χ² = (200 - 180)²/180 + (150 - 180)²/180 + (50 - 40)²/40
    + (250 - 270)²/270 + (300 - 270)²/270 + (50 - 60)²/60
Χ² = 400/180 + 900/180 + 100/40 + 400/270 + 900/270 + 100/60
Χ² = 2.22 + 5.00 + 2.50 + 1.48 + 3.33 + 1.67 = 16.2

As you can see, the math gets a bit cumbersome, so I did it for you!  

a & b) State the null and alternative hypotheses: Ho ___?___ , Ha ___?___

c. Which specific type of chi square test was used for this analysis? ___?___

d. What are the degrees of freedom used for this problem (columns -1)(rows -1) = df = ___?___

e. So, the P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than (enter a value) ___?___

The P-value was calculated for you: P(Χ2 > 16.2) = 0.0003

f. Based on the given information, interpret the results in symbols and values ________

g. Then interpret the results in words (full sentence) ___________

h. What will the distribution look like on a Bell curve? ____________

The number of pig farms is increasing, a study was conducted to test if composted pig manure might be a better fertilizer than composted cow manure. Eight corn fields of equal size were chosen for the experiment. One half of each corn field was fertilized with composted cow manure and the other half was fertilized with composed pig manure. The yields are given in the following table.

Test at a = 0.01 the claim that the average yield is higher for composted pig manure than it is for composted cow manure.

Some critics of big business argue that CEOs are overpaid and that their compensation is not related the performance of their company. To test this theory, data on executive's total pay and company's performance was collected from a randomly selected set of fifty companies.

A. Identify the independent variable(s) - If any (and define them precisely and indicate whether they are qualitative or quantitative).

B. Identify the dependent variable - if any (and define them precisely and indicate whether they are qualitative or quantitative).

C. Identify the type of analysis that is appropriate (Chi- Square test of independence, ANOVA, Regression, or Correlation)

D. Justify why the analysis you identified in part C is correct.

a. What is hypothesis testing in statistics? Discuss

b. Does Type I error being considered more serious than Type II error? Explain

c. What is the p-value of a test? Give an example

Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the best point estimate for μ, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed.

A 95% confidence interval for μ using the sample results x= 94.6, s= 6.9, and n =42

Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.

point estimate =

margin of error =

the 95% confidence interval =

Read the following description and then answer items 12 to 16: Researchers are interested in determining if there is a difference between two exercise regimens (A and B). The researchers think that the regimens may have differential effects on a treadmill test where the participants run to exhaustion.

12.Write the appropriate null hypothesis.

14. What is the dependent variable in this study?

16. Describe what happens if the researchers make a type II error.

Consider a manufacturing process that produces cylindrical component parts for the automotive industry. According to specifications, it is important that the process produces parts having a mean diameter of 5.0 millimeters. An experiment is conducted in which 100 parts produced by the process are selected randomly and the diameter measured on each part. It is known that the population standard deviation is 0.1. It was found that the sample mean diameter is 5.027 millimeters. The process engineer Mr. Tan would like to find out how likely is it that one could obtain a sample mean diameter of at least 5.027 with sample size n = 100, if the population mean µ = 5.0. Apply the concept of central limit theorem. Mr Tan claimed that “In only 7 in 1000 experiments, one would experience by chance a sample mean that deviates from the population mean by as much as 0.027.” Do you agree? Explain your reasoning.

So, I am conducting a research project and I have many categorical variables that I am trying to run crosstab and chi-square tests on. The only issue is that I only recieved 81 respondents so a lot of my questions have less than 5 people who selected one answer over another. I am unsure what to do. Do I state in my discussion section that due to there being a lack of respondents that I could not test for significance on many of my variables? Or, is there another test that I can run that I am not thinking of?

In a quiz show a uniformly random integer r between 1 and 10 is generated. Another, independent such random numbers will then be generated, but before that happens, you are invited to guess whether s will be greater than or less than r. If you are correct, then you win s pounds. If you lose (or if s = r) then you win nothing. (i) Clearly if r = 1 you should guess that s will be larger. And if r = 10 you should guess that s will be smaller. At which value of r should your strategy change from guessing s will be larger to guessing it will be smaller? (Your aim, as always, is to maximise your expected gain.) (ii) Suppose now that the range of possible values for r and s is 1, ... , N. Then in the limit as N tends to infinity the change of strategy should happen at a value of r of approximately N/k. Find the value of k.

The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.]

The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal places. Use the letter ?x to represent the value of the temperature.)

?̂ =_____

Use the equation of the least‑squares regression line to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 2525 degrees Celsius. Enter your answer rounded to two decimal places.

beak heat as a percent of total body heat loss=beak heat as a percent of total body heat loss=_____%

What percent of the variation in beak heat loss is explained by the straight-line relationship with temperature? Enter your answer rounded to two decimal places.

percent of variation in beak heat loss explained by the equation=percent of variation in beak heat loss explained by the equation=_____%

Find the correlation ?r between beak heat loss and temperature. Enter your answer rounded to three decimal places.

?=_____

A safety light is designed so that the times between flashes are normally distributed with a mean of 5.00s and a standard deviation of 0.40s

a. Find the probability that an individual time is greater than 5.50s

b. Find the probability that the mean for 60 randomly selected times is greater than 5.50s

c. Given that the light is intended to help people see an​ obstruction, which result is more relevant for assessing the safety of the​ light?

At a certain university, 50% of all entering freshmen planned to major in a STEM (science, technology, engineering, mathematics) discipline. A sample of 36 freshmen is selected. What is the probability that the proportion of freshmen in the sample is between 0.482 and 0.580? Write the answer as a number to the 4th decimal (0.1234).

The intended steps are as follows:

Step 1: Check to see that the conditions np ≥ 10 and n(1− p) ≥ 10 are
both met. If so, it is appropriate to use the normal curve.
Step 2: Find the mean U_p and standard deviation a_p.
Step 3: Sketch a normal curve and shade in the area to be found.
Step 4: Find the area using the TI-84 PLUS.