1. You are a nursing researcher and you are interested in whether university grades are predictive of performance on the NCLEX exam. You randomly select a sample of 25 nurses from the Ontario registry and obtain each nurse’s score on the NCLEX examination. You also have access to their final grade in university. The complete data are shown in the table below. Use these data to answer the questions below the table. Assume a 0.05 level of significance.

1. Use SPSS to obtain the predictive equation. Provide the equation and the supporting SPSS output. [1 Mark]

2. Use an appropriate statistic provided by the SPSS output to describe the utility (goodness) of the regression equation for predicting NCLEX scores. [1 Mark]

3. What is the predicted NCLEX score for a final grade = 75? [1 Mark]

4. What is the unexplained variation in NCLEX scores for your regression model? Show your calculation. [1 Mark]

A research service estimates that the mean annual consumption of fresh market tomatoes by a person in the US is atleast 21 pounds. You doubt this claim. A simple random sample of 23 people in the US has a mean annual consumption of fresh market tomatoes of Xbar=19 pounds and a standard deviation of 4 pounds. Assume the pop. is normally distributed. Construct the appropriate hypothesis and conduct the test at the 1% level of significance. Based on the Critical Value approach is there enough evidence to reject the claim?

A nutrition lab tested 40 randomly selected hot dogs to see if their mean sodium content was less than 325mg upper limit set by regulations for "reduced sodium" franks. The sample yielded a mean of 322 mg with a standard deviation of 11.5 mg.

A) To construct a confidence interval, would you use a z-chart or a t-chart? why?

B) Construct a 90% confidence interval for for estimating the mean sodium content for "reduced sodium" hot dogs. Interpret the confidence interval in a sentence.

C) Test the claim that the mean sodium level for the "reduced sodium" hot dogs is less than the limit of 325mg. Use a significance level of 0.05.

D) Does the confidence interval support the conclusion of the hypothesis test? Explain.

The density of an oil mixture (mix) as a function of the temperature (T) and the mass fraction of the three components (mi) was measured and results are shown :

T (K) m1 m2 m3 Pmix (kg/m3 )

300 0 1 0 879.6

320 0 0.5 0.5 870.6

340 0 0 1 863.6

360 0.5 0 0.5 846.4

380 0.5 0.25 0.25 830.8

400 0.5 0.5 0 819.1

420 1 0 0 796

440 1 0 0 778.2

Find the coefficients for a multiple regression of the form Pmix = a0 + a1*T + a2*m1 + a3*m2 + a4*m3

Researchers conducting a clinical trial randomly assigned 60 patients with painful knee osteoarthritis evenly into one of three treatment groups: glucosamine, chondroitin, or placebo.After the study period, patients were asked if they experienced substantial improvement in pain and ability to function normally.Thirty-four patients replied that they did have an improvement, including 13 in the glucosamine group, 16 in the chondroitin group, and 5 in the placebo group.

List a potential confounding variable for this study and briefly explain a possible consequence it could have on the results.

Topic: “Is there a different between teacher’s and parents’ perceptions of what constitutes effective school-to-home communication?”

Ho: this is the currently accepted statement that there is no significant difference between teachers and parents’ perceptions of what constitutes effective school-to home communication.

Ha: this is my research hypothesis that is making the statement that there is a significant difference between teacher’s and parents’ perceptions of what constitutes effective school-to-home communication.

Ho & Ha are opposite mathematically, thus the possible outcomes of this investigation is to

1. Reject the null hypothesis
2. Fail to reject the null hypothesis

How do the findings fail to reject or reject the null hypothesis?

1. Test Statistic- to calculate from sample data
2. Statistically Significant- making a decision
3. Level of Confidence- C- 95% , 99%

We have three light bulbs with lifetimes T1,T2,T3 distributed according to Exponential(λ1), Exponential(λ2), Exponential(λ3). In other word, for example bulb #1 will break at a random time T1, where the distribution of this time T1 is Exponential(λ1). The three bulbs break independently of each other. The three light bulbs are arranged in series, one after the other, along a circuit—this means that as soon as one or more light bulbs fail, the circuit will break. Let T be the lifetime of the circuit—that is, the time until the circuit breaks.

(a) What is the CDF of T, the lifetime of the circuit?

(b) Next, suppose that we only check on the circuit once every second (assume the times T1,T2,T3,T are measured in seconds). Let S be the first time we check the circuit and see that it’s broken. For example, if the circuit breaks after 3.55 seconds, we will only observe this when 4 seconds have passed, and so S = 4. Calculate the PMF of S.

(c) Finally, suppose that instead of checking on the circuit every second, we instead do the following: after each second, we randomly decide whether to check on the circuit or not. With probability p we check, and with probability 1−p we do not check. This decision is made independently at each time. Now let N be the number of times we check and see the circuit working. For example, if the circuit breaks at time 3.55, and our choices were to check at time 1 second, not to check at times 2 or 3 or 4, and to check at time 5, then N = 1, since the circuit was broken the 2nd time we checked. What is the PMF of N? (Hint: start by finding the joint PMF of N and S. It’s fine if your answer is in summation form.)

A nutritionist is interested in the relationship between cholesterol and diet. The nutritionist developed a non-vegetarian and vegetarian diet to reduce cholesterol levels. The nutritionist then obtained a sample of clients for which half are told to eat the new non-vegetarian diet and the other half to eat the vegetarian diet for three months. The nutritionist hypothesizes that the non-vegetarian diet will reduce cholesterol levels more. What can the nutritionist conclude with α = 0.01. Below are the cholesterol levels of all the participants after three months.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Condition 1:
---Select--- cholesterol level non-vegetarian months diet vegetarian
Condition 2:
---Select--- cholesterol level non-vegetarian months diet vegetarian

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;  ---Select--- na trivial effect small effect medium effect large effect
r² =  ;  ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

Non-vegetarians had significantly higher cholesterol levels than vegetarians.

Non-vegetarians had significantly lower cholesterol levels than vegetarians.    

There was no significant cholesterol difference between non-vegetarians and vegetarians.

Prove "The Birthday Problem" in this regard,

Suppose there are some number of people in a room and we need need to consider all possible pairwise combinations of those people to compare their birthdays and look for matches.Prove the probability of the matches.

In this problem, we use your critical values table to explore the significance of r based on different sample sizes. (a) Is a sample correlation coefficient ρ = 0.82 significant at the α = 0.01 level based on a sample size of n = 3 data pairs? What about n = 14 data pairs? (Select all that apply.) No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 14 and α = 0.01. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 3 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 3 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 3 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 14 and α = 0.01. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 3 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 14 and α = 0.01. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 14 and α = 0.01. Incorrect: Your answer is incorrect. (b) Is a sample correlation coefficient ρ = 0.42 significant at the α = 0.05 level based on a sample size of n = 18 data pairs? What about n = 26 data pairs? (Select all that apply.) Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 26 and α = 0.05. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 26 and α = 0.05. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 26 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 18 and α = 0.05. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 18 and α = 0.05. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 26 and α = 0.05. Incorrect: Your answer is incorrect. (c) Is it true that in order to be significant, a ρ value must be larger than 0.90? larger than 0.70? larger than 0.50? What does sample size have to do with the significance of ρ? Explain your answer. No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant. No, sample size has no bearing on whether or not the correlation coefficient might be significant. Yes, a larger correlation coefficient of 0.70 means that the data will be significant. Yes, a larger correlation coefficient of 0.90 means that the data will be significant. Yes, a larger correlation coefficient of 0.50 means that the data will be significant.

Book :Business Analytics 6^th edition (data analysis and decision making)

By s. Chirstian albright and wayne. L . w

A

If your company makes a particular decision in the face of uncertainty, you estimate that it will either gain $10,000, gain $1000, or lose $5000, with probabilities 0.40, 0.30, and 0.30, respectively. You (correctly) calculate the EMV as $2800. However, you distrust the use of this EMV for decision-making purposes. After all, you reason that you will never receive $2800; you will receive $10,000, $1000, or lose $5000. Discuss this reasoning.

B

In the previous question, suppose you have the option of receiving a check for $2700 instead of making the risky decision described. Would you make the risky decision, where you could lose $5000, or would you take the sure $2700? What would influence your decision?

C

A potentially huge hurricane is forming in the Caribbean, and there is some chance that it might make a direct hit on Hilton Head Island, South Carolina, where you are in charge of emergency preparedness. You have made plans for evacuating everyone from the island, but such an evacuation is obviously costly and upsetting for all involved, so the decision to evacuate shouldn’t be made lightly. Discuss how you would make such a decision. Is EMV a relevant concept in this situation? How would you evaluate the consequences of uncertain outcomes

When using the test for homogeneity of variance, basically four outcomes or options can be considered if a violation of the homogeneity of variance assumption is violated. These include:

Option 1: Since a violation of the homogeneity of variance assumption occurred, the independent t-test may not be the appropriate statistical procedure for analysis of data. Therefore, we may opt for a lower order non-parametric statistical test.

Option 2: Since a violation of the homogeneity of variance assumption occurred, the independent t-test may not be the appropriate statistical procedure for analysis of data. Therefore, we will abandon the test all together.

Option 3: Even though we violated the homogeneity of variance assumption, we will continue to use the parametric measure due to the robust nature of the tests.

Option 4: Resample with a larger sample size and retest.

Provide MULTIPLE pros and cons of each of the four options and which one you think is the most valid.

Please answer ALL the questions (as there are multiple) embedded in the above task.

Q 1 . ( 8 marks) Answer the following:

a) Describe the difference between a discrete and a continuous ra ndom variable. Give an example of each.

b) Under what conditions might you choose to use a dot plot rather than a histogram?

c) Differentiate between retrospective and observational studies

d) What is the significance of the Bayes’ Theorem?   

For a poisson distribution where X ~ Pois(u), solve the questions below. Please show all work and all steps.

a.) Show that the pmf is a pmf using the criteria for verifying pmf (2 conditions).

b.) Show that E(X) = u

c.) Show that Var(X) = u