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 __

The following data contains the data for a group of participants that took a timed test. The data are the average amount of time the participants took on each item (response time) and the number of guesses it took to get each item correct (number correct).

Do this using SPSS; make sure you show your output data as well as your responses to the following questions.

A. What is the regression equation for predicting response time from number correct?

B. What is the predicted response time if the number correct is 8?

C. Based upon the p-value, would you reject the null or accept the null? Explain your decision and what this tells us.

The Tire Rack, America's leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle. The following data show survey ratings (1 to 10, with 10 being the highest) for 18 summer tires. Develop an estimated regression equation that can be used to predict the Buy Again rating given based on the Steering and Tread wear rating. How many percent of the variation in the Buy Again variable could be predicted by Steering and Thread wear rating?

Note: put answers into decimal form, if your answer is 90.8765%, enter in 0.908765.

You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 9.

Find the critical value that corresponds to a confidence level of 98%. Report answer accurate to three decimal places with appropriate rounding.