## Hypothesis Testing: SPSS Tables

You are interested in understanding whether the average Lifetime Value (the net present value of all the transaction expected from a customer) for the customers in the Floridais significantly different from those in California. You suspect that the CaliforniaLTV (Lifetime value) would be higher than in Florida. In order to test this hypothesis, you pick 10 customers each in the California and Florida and record their LTV(in dollars). The data is in LTV.sav. State the appropriate hypothesis, run the appropriate test using SPSS and provide interpretation.

## A hospital group operates 33 clinics in Indiana and Illinois

Please show all steps:

A hospital group operates 33 clinics in Indiana and Illinois. A study was conducted to estimate the difference in mean time spent per visit for men and women. Previous studies indicated that the standard deviation is 11 min, for men and 16 min. for women. A random sample of 100 men and 100 women at the two states was observed. The resulting sample means were 34.5 min. for men and 42.4 min. for women. Is the difference between men and women significant at ? = 0.05

a. State null & alternate hypotheses

Null hypothesis: H0: µ1 = µ2

Alternate hypothesis H1: µ1 ? µ2

b. What is the ‘degree of freedom’?

c. Calculate t test statistic

d. Determine t critical

e. Is the difference in mean time between men and women significant?

## Hypothesis Testing:Statistics on English composition course

A local college requires an English composition course for all freshman. This year they are evaluating a new online version of the course. A random sample of n=16 freshman is selected and the students are placed in the online course. At the end of the semester, all freshman take the same English composition exam. The average score for the same is M=76. For the general population of freshman who took the traditional lecture class, the exam scores form a normal distribution with a mean of µ=80.

a-if the final exam scores for the population have a standard deviation of 12, does the sample provide enough evidence to conclude that the new online course is significantly different from the traditional class? Assume a two-tailed test with and alpha =.05.

b-if the population standard deviation is 6, is the sample sufficient to demonstrate a significant difference? Again, assume a two-tailed test with and alpha =.05.

c-comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.

## Conducting statistics for herbal remedies

Although there is a popular belief that herbal remedies such as ginkgo biloba and ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research. In a typical study, a researcher obtains a sample of n=36 participants and has each person take the herbal supplements every day for 90days. At the end of the 90 days, each person takes a standardized memory test. For the general population, scores fromt he test are normally distributed with a mean of 80 and a standard deviation of 18. The sample research participants had an average of M=84.

a-assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variables being examined.

b-using symbols, state the hypothese (Ho and H1)for the two-tailed test.

c-sketch the appropriate distribution, and locate the critical region for alpha=.05

d-calculate the test statistic (z-score) for the sample.

e-what decision should be made about the null hypothesis, and what decision should be made about the effect of the herbal supplements.

## Hypothesis Testing & Confidence Interval: M&M Candies

Construct a 95% confidence interval for the proportion of red candies.

Using your same data determine if the proportion of green candies in a package of M&Ms is different than what is claimed by the company. List null and alternative hypothesis, the test-statistic and the p-value.

If you wanted to estimate the proportion of a certain color of candy to within 2% of the actual proportion, how many individual pieces of candy must you sample. Assume you want to be 90% confident in your results. How many packages of candy based on the total count of candies in your package would be required?

My bag contained: blue-5, brown-3, green-4, orange-5 red-1, yellow-3

MARS Company claims this color distribution by packet. blue-23% brown-12%, green 15%, orange 23%, red 12%, yellow 15%.

## Is Correlational study a good choice?

I have to develop a research design for a pretend study. It will be quantitative to study the effects of linguistic modification on nursing exams for one year. The original exam and the modified exam will be randomly assigned to students (native English speakers and English as a second language students). There would be scores from four groups to compare:

native English speakers recieving the original exam

English as a second language receiving the original exam

native English speakers recieving the modified exam

English as a second language recieving the modified exam

I have no idea what kind of quantitative analysis to use for this. Would this be correlational? If you have a better idea please tell me as I am stuck.

Assessment strategies in nursing education need to respect the diverse student population. Multiple-choice examinations are a popular assessment tool because they reflect the type of questions that make up the national licensure exam. However, small qualitative studies have shown that linguistic bias is a determent to English as a second language (ESL) and culturally diverse students’ success in nursing programs and in passing the national licensure examination. This study will quantitatively determine if there is a difference between successes on linguistic modified exams and ESL students and the non-modified exams. The study will also show whether the native English speaking (NS) fairs better on the modified exam.

One exam will be the regular exam given in class

the other will be “modified” so there is no language bias in the exam

Example: regulare exam might say “the patient was drinking gatoraid for his clear liquid diet” and ESL and culturally diverse students might not know what gatoraid is

whereas a native who grew up here would know gatoraid is a clear liquid.

## Correlation questions

1. For the following scores,

X Y

3 6

6 1

3 4

3 3

5 1

a) Find the regression equation for predicting Y from X

b) Calculate the predicted Y value for each X

2. For the following scores

X Y

1 6

4 1

1 4

1 3

3 1

a) Compute the Pearson correlation

3. Identifying individuals with a high risk of Alzheimer’s disease usually involves a long series of cognitive tests. However, researcher have developed a 7-Minute Scree, which is a quick and easy way to accomplish the same goal. The question is whether the 7-Minute Screen is as effective as the complete series of tests. To address this question, Ijuin et al. (2008) administered both tests to a group of patients and compared the results. The following data represent results similar to those obtained in the study.

Patient 7-Minute Screen Cognitive Series

A 3 11

B 8 19

C 10 22

D 8 20

E 4 14

F 7 13

G 4 9

H 5 20

I 14 25

a) Compute the Pearson correlation to measure the degree of relationship between the two scores.

b) Is the correlation statistically significant? Use a two-tailed test with an alpha=.01

c) What percentage of variance for the cognitive scores is predicted from the 7-Minute Screen scores? (Compute the value of r2 )

## Ravencheck Resources, Inc. is a brokerage of ten salespeople

Ravencheck Resources, Inc. is a brokerage of ten salespeople. A productivity survey of the firm’s employees indicated the following data:

Sales Representative Number of units Sold Number of Sales

A 28 14

B 66 35

C 38 22

D 70 29

E 22 6

F 27 15

G 28 17

H 47 20

I 14 12

J 68 29

Use the information from the survey. Assume that “number of sales calls” is the independent variable, and draw a scatter diagram of number of sales calls and number of units sold. Estimate a simple linear regression model to explain the relationship between number of sales calls and number of units sold. Calculate and interpret the coefficient of correlation, the coefficient of determination, and the standard error of estimate. Conduct a test of hypothesis to determine whether the coefficient of correlation in the population is zero. Construct and interpret confidence intervals and prediction intervals for the dependent variable, number of units sold.

## Sample proportion question

When an election for political office takes place, the television networks cancel regular programming and instead provide election coverage. When the ballots are counted, the results are reported. However, for important offices such as president or senator in large states, the networks actively compete to see which will be the first to predict a winner. This is done through exit polls, wherein a random sample of voters who exit the polling booth is asked for whom they voted. From the data, the sample proportion of voters supporting the candidates is computed. Hypothesis testing is applied to determine whether there is enough evidence to infer that the leading candidate will garner enough votes to win. Suppose that in the exit poll from the state of Florida during the 2000 year elections, the pollsters recorded only the votes of the two candidates who had any chance of winning, Democrat Al Gore and Republican George W. Bush. In a sample of 765 voters, the number of votes cast for Al Gore was 358 and the number of votes cast for George W. Bush was 407. The network predicts the candidate as a winner if he wins more than 50% of the votes. The polls close at 8:00 P.M. Based on the sample results, should the networks announce at 8:01 P.M. that the Republican candidate George W. Bush will win the state? Select a level of significance by analyzing Type I and Type II errors and clearly show your analysis.

## Concepts and properties of the hypothesis testing.

1.

a) What is a hypothesis? Specifically, is it a statement about the population or the sample?

b) What is the purpose of hypothesis testing?

c) How is the role of the null hypothesis different from that of the research (alternative) hypothesis?

d) Provide an example of a hypothesis test you could conduct at work. What is the measure that you will test?

2.

a) What assumptions must be satisfied for a two-sided (non-directional) hypothesis test to be valid?

b) If an assumption was not satisfied, what, if anything, could be done to fix the problem?

c) Provide an example from your workplace or personal life of a two-sided hypothesis test.

## Hypothesis Testing Exercise

M&Ms® Project

Part 5

Test the hypothesis (α = 0.05) that the population proportions of red and brown are equal (pred = pbrown). You are testing if their proportions are equal to one another, NOT if they are equal to one another AND equal to 13%. NOTE: These are NOT independent samples, but we will use this approach anyway to practice the method. This also means that n1 and n2 will both be the total number of candies in all the bags. The “x” values for red and brown are the counts of each we found on the Data page. We will need to calculate the weighted p:

State clear hypotheses, test statistic, critical value or p-value, decision (reject/fail to reject), and conclusion in English.

We can use StatCrunch or the TI to help with this test. Needed information for both tools include:

x1 = number of red

n1 = total number of candies

x2 = number of brown

n2 = total number of candies

For the TI, you will want 2-PropZTest. Then select the appropriate alternative (not equal), and Calculate then enter. The output will have the test statistic (z), p-value (p), sample p values, weighted p ( ), then repeat of sample sizes.

For StatCrunch, we will select Stat > Proportions > Two Sample > with summary. The output will contain the test statistic (Z-Stat) and p-value.

At the end of this project, we will be writing a report, explaining the method and presenting the results from each part of the project.

## Case 3: Grocery4You.com

e-grocers are companies that sells groceries over the internet. Customers open an online account, enter their orders, pay by credit card or debit card, and receive deliveries by truck. Several businesses think that it is means of convenience for busy customers who have no or very little time to go to a grocery store, buy groceries, and wait in line to pay – not to mention the driving time to and from the grocery store. In the year 2001, two of America’s largest online supermarkets – Webvan.com on the West Coast and HomeRuns.com on the East Coast – abruptly shut down . They left behind at least 2,000 people without jobs and irate customers who thought that the service of all things cyber, seemed like a sure bet.1 The investors lost their money. Learning lessons from history, Grocery4You.com, a potential e-grocer is planning cautiously on the prospects of starting the e-grocery business. A team of entrepreneurs wants to thoroughly research the prospects of staying in business and being profitable prior to starting it. They analyzed the market and determined that the average order would have to be $84 to breakeven (cover the costs) and any further increase in an average order would generate a profit. As a pilot, the team offers the e-grocery service in one large city. Although the entrepreneurs have an MBA, statistical (data) analysis was their weakness in school. They relied on other team members to complete the assignments thinking “What’s the point? I am never going to use this.” They hire your team as an analyst to validate the possibility of being profitable. Statistics was your favorite subject in school because your funny instructor combined theory with applications making the subject interesting. You welcome this opportunity to apply some statistical analysis you learned in school on this project. You know from your statistics education that inferential statistics begins with collecting a sample. You record the size of the order for a random sample of customers from this large city in the Excel spreadsheet. Based on this data, can you convince the team of entrepreneurs that the business will be profitable? Also analyze and present Type I and Type II errors to select the level of significance.

## Statistics – Critical Values

Write the claim mathematically and identify Hₒ and Hₐ. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) decide whether to reject or fail to reject the null hypothesis.

A medical researcher says that at least 24% of adults are smokers. In a random sample of 160 adults, 22.5% say they are smokers. At ἀ = 0.01, do you have enough evidence to reject the researcher’s claim?

(a) Which of the following correctly states Hₒ and Hₐ?

(b) What is (are) the critical value(s) z ₒ?

z ₒ = _____ (use a comma to separate answers as needed. Round to two decimal places as needed)

Which of the following graphs has the rejection region(s) shaded correctly?

(c) What is the standardized test statistic? z = _____ (round two decimal places as needed)

(d) Which of the following is the correct conclusion for the test?

___Reject Hₒ. There is enough evidence to reject the claim that at least 24% of adults are smokers.

___ Reject Hₒ. There is not enough evidence to reject the claim that at least 24% of adults are smokers.

___ Fail to reject Hₒ. There is not enough evidence to reject the claim that at least 24% of adults are

smokers.

___ Fail to reject Hₒ. There is enough evidence to reject the claim that at least 24% of adults are

smokers.

## Hypothesis Testing: One Sample Inference

You are doing a study examining the effects of studying method on academic achievement. All the students in your study take a course on genetics that lasts for 10 days. One group of students studies 20 minutes a day for 10 days. The second group studies once at the end of the course but for 200 minutes.

What is a one-tailed test? What is a two-tailed test? Explain at least three differences between one- and two-tailed tests.

State a hypothesis related to this study that would cause you to conduct a one-tailed test. State a hypothesis related to this study that would cause you to conduct a two-tailed test.

## One-tailed and Two-tailed Tests

You are doing a study examining the effects of studying method on academic achievement. All the students in your study take a course on genetics that lasts for 10 days. One group of students studies 20 minutes a day for 10 days. The second group studies once at the end of the course but for 200 minutes.

What is a one-tailed test? What is a two-tailed test? Explain at least three differences between one- and two-tailed tests.

State a hypothesis related to this study that would cause you to conduct a one-tailed test. State a hypothesis related to this study that would cause you to conduct a two-tailed test.