You are considering testing a new drug that is supposed to facilitate learning in mentally retarded children. Based on preliminary research, you have some idea about the size of the drug's effect. Because of your work schedule you can either do the test with 15 subjects or with 20. You would like to only run 15 subjects, but if running 20 will make power at least 20% higher, you will run 20 subjects. Calculate power for the following conditions: a. N = 15, a = .051 tail, Preal = 0.70. b. N = 20, a = .051 tail, Preal = 0.70. c. Based on your calculations, how many subjects will you test?

The accompanying data are the shoe sizes and heights​ (in inches) of

14

men. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. If the​ x-value is not meaningful to predict the value of​ y, explain why not.

Tomato weights and Fertilizer: Carl the farmer has three fields of tomatoes, on one he used no fertilizer, in another he used organic fertilizer, and the third he used a chemical fertilizer. He wants to see if there is a difference in the mean weights of tomatoes from the different fields. The sample data is given below. The second table gives the results from an ANOVA test. Carl claims there is a difference in the mean weight for all tomatoes between the different fertilizing methods.

Tomato-Weight in Grams

ANOVA Results

The Test: Complete the steps in testing the claim that there is a difference in the mean weight for all tomatoes between the different fertilizing methods.(a) What is the null hypothesis for this test?

H₀: At least one of the population means is different from the others. H₀: μ₁ ≠ μ₂ ≠ μ₃.     H₀: μ₁ = μ₂ = μ₃. H₀: μ₃ > μ₂ > μ₁.

(b) What is the alternate hypothesis for this test?

H₁: μ₁ ≠ μ₂ ≠ μ₃. H₁: μ₁ = μ₂ = μ₃.     H₁: μ₃ > μ₂ > μ₁. H₁: At least one of the population means is different from the others.

(c) What is the conclusion regarding the null hypothesis at the 0.05 significance level?

reject H₀ fail to reject H₀    

(d) Choose the appropriate concluding statement.

We have proven that all of the mean weights are the same. There is sufficient evidence to conclude that the mean weights are different.     There is not enough evidence to conclude that the mean weights are different.

(e) Does your conclusion change at the 0.01 significance level?

Yes No    

Given two independent random samples with the following results: n1=18x‾1=141s1=13   n2=12x‾2=161s2=12

Use this data to find the 98% confidence interval for the true difference between the population means. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 2 of 3 : Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Schoneberger and Cukier define “Big Data” as “more, messy, and good enough”. Explain each of these concepts with an example for each

Differentiate between correlation and causality. Give an example to illustrate the difference.

Why is the question of privacy worth revisiting in the era of Big Data? In particular identify at least three aspects that have changed over the last 10 years

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 90% confidence interval for μ using the sample results x= 134.0, s= 55.6, and n= 50

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 90% confidence interval =

How has “Big Data” and analytics impacted health care? Explain with at least three practical examples

Question 6: Analytics Concepts

1. What is a “model” in terms of predictive data analysis? Give an example.
2. How will you explain the concept of hypothesis testing to a layperson?
3. What is the difference between Mean and Median? If you could pick only one number to explain the salaries of NBA players, which one will you pick and why?
4. “With big data we can escape the straightjacket of group identities and replace them with much more granular predictions for each individual.
   The promise of big data is that we do what we’ve been doing all along – profiling – but make it better, less discriminatory and more individualized.” Argue a case for or against this new type of behavioral profiling.

A market research firm conducts telephone surveys with a 43% historical response rate.

a. What is the probability that in a new sample of 400 telephone numbers, at least 160 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 160/400 = 0.4?

Calculate the standard error to 4 decimals.  
Calculate the probability to 4 decimals, showing your steps along the way.
P( ≥  ) = P(z ≥  ) =  

b. If a follow-up study was completed a year later with only 64 telephone numbers, what is the probability that the response rate was between 39% and 48%?
Calculate the standard error to 4 decimals.  
Calculate the probability to 4 decimals, showing your steps along the way.
P(  ≤  ≤  ) = P(  ≤ z ≤  ) =   -   =  

Lisa is at a bus stop. The times between successive bus arrivals are independent and identically distributed exponential random variables with mean 3 minutes. While lisa is waiting, Mindy calls to say she will arrive in exactly 3 minutes. Lisa will wait for Mindy and they will ride a bus together. Calculate the probability that Lisa will miss the first and both Lisa and Mindy will catch the second bus.

USE CALCULATOR AND SHOW EVERYSTEP USING CALCULATOR INCLUDING THE NUMBERS USE INPUT IN THE TEST. New road signs are made with the intention of improving visibility for drivers. Highway safety engineers setup a test course that included both the old and new signs. Volunteers drove the course and rated the old and new signs in terms of visibility? (2 points each)

a) Write the null and alternative hypotheses in words using “improved visibility” and “not improved visibility”.

b) Describe a Type I error in the context of the problem.

c) What would be the real-world consequences be if a Type I error occurred?

d) Describe a Type II error in the context of the problem.

e) What would be the real-world consequences be if a Type II error occurred?

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 800 grams while babies born after a gestation period of 40 weeks have a mean weight of 3300 grams and a standard deviation of 425 grams. If a 35​-week gestation period baby weighs 2475 grams and a 40​-week gestation period baby weighs 2975 ​grams, find the corresponding​ z-scores. Which baby weighs less relative to the gestation​ period?

The baby born in week __ weighs relatively less since it's z- score, __, is larger than the z-score of __ for the baby born in week __