## Conducting a 5-step Hypothesis Testing

Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the 5 steps of hypothesis testing listed below, what should the experimenter conclude?

Step 1 (Restate the Question as a research hypothesis and null hypothesis about the populations)

Population 1:

Population 2:

Research Hypothesis

Null Hypothesis

Step 2 (Determine the characteristics of the comparison distribution)

Estimated population variance for population 1

Estimated population variance for population 2

Pooled estimate of the population variance

Variance of distribution of means for population 1

Variance of distribution of means for population 2

Variance of distribution of differences between means

SD of distribution of differences between means

Step 3 (Using the .05 level, determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected)

Probability

Type of test (one or two tailed)

Degrees of freedom total

Cutoff score

Step 4 (Determine your sample’s score on the comparison distribution)

t score:

Step 5 (Decide whether to reject the null hypothesis).

## Performing a 5-step hypothesis testing

Do students at various universities differ in how sociable they are? Twenty-five students were randomly selected from each of three universities in a region and were asked to report on the amount of time they spent socializing each day with other students. The result for University X was a mean of 5 hours and an estimated population variance of 2 hours; for University Y, M = 4, S2 = 1.5; and for University Z, M = 6, S2 = 2.5. Using the 5 steps of hypothesis testing listed below, what should you conclude? (Refer to page 319 in the text for steps to complete this problem).

Step 1 (Restate the Question as a research hypothesis and null hypothesis about the populations)

Population 1:

Population 2:

Population 3:

Research Hypothesis:

Null Hypothesis:

Step 2 (Determine the characteristics of the comparison distribution)

df between:

What distribution?:

Step 3 (Using the .05 level, determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected)

Probability:

Degrees of freedom:

Cutoff score:

Step 4 (Determine your sample’s score on the comparison distribution)

Between groups population variance estimate:

Within groups population variance estimate :

F:

Step 5 (Decide whether to reject the null hypothesis)

Figure the effect size for the study

## Z Test and ANOVA

1. An Ivy League college is concerned that out of state students may be receiving lower grades than the state residents students. Two independent random samples have been selected: 165 observations from population 1 (Out of state students) and 177 from population 2 (State students). The sample means obtained are X1(bar)=86 and X2(bar)=87. It is known from previous studies that the population variances are 8.1 and 7.3 respectively. Using a level of significance of .01, is there evidence that the out of state students may be receiving lower grades? Fully explain your answer

2. I drive to work every weekday. I have three options to drive there. I can take the Toll Road, or I can take a main highway with some traffic lights, or I can take the back road, which has no traffic lights but is a longer distance. Is there is a difference in the time it takes to drive each route?

I randomly selected the route on 21 different days and wrote down the time it took me for the round trip, getting to work in the morning and back home in the evening. At the .01 significance level, can I conclude that there is a difference between the driving times using the different routes?

## Hypothesis testing, confidence interval for mean and proportion

A snack food company produces bags of peanuts labeled as containing 4 ounces. A consumer reports organization wants to see if the weight is actually less than 4 ounces. They randomly choose 40 bags and their contents are weighed. They find the average weight is 3.5 ounces with a standard deviation of s = 0.9 ounces. Is this sufficient evidence to conclude that the bags contain less than 4 ounces of peanuts?

a. State the null and alternative hypotheses.

H0:

Ha:

b. What is the value of the one-sample t statistic? Do not pool variances.

t = Round to 3 places.

c. What is the P-value for the t test?

P-value = Round to 4 places.

d. Is there sufficient evidence that the bags contain less than 4 ounces of peanuts?

e. Give a 95% confidence interval for the mean weight of peanuts in each bag. (The t critical value is 2.009.)

From ounces to ounces. Round each number to 2 places.

2-

Simple random sample of high-interest mortgages and low-interest mortgages were obtained. For the 61 high-interest mortgages, the borrowers had a mean FICO credit score of 585 and a standard deviation of 51.5. For the 22 low interest mortgages, the borrowers had a mean FICO score of 636 and a standard deviation of 36.8. Test the claim that the mean FICO score of borrowers with high-interest mortgages is lower than the mean FICO score of borrowers with low-interest mortgages.

a. State the null and alternative hypotheses.

H0:

Ha:

b. What is the value of the two-sample t statistic? Do not pool variances.

t = Round to 3 places.

c. What is the P-value for the t test? Use degrees of freedom of 21 or technology.

P-value = Round to 4 places.

d. Does the FICO credit rating score appear to affect mortgage payments?

o There is sufficient evidence to show that the mean FICO score of borrowers with high-interest mortgages is lower than the mean FICO score of borrowers with low-interest mortgages.

o There is not sufficient evidence to show that the mean FICO score of borrowers with high-interest mortgages is lower than the mean FICO score of borrowers with low-interest mortgages.

e. Give a 90% confidence interval for the mean difference between FICO scores of high-interest and low-interest borrowers. Answer using technology or if completed by hand use degrees of freedom of 52.05.

From a score of __ to a score of ____ . Round each number to 2 places.

3-

According to the National Institute on Alcohol Abuse and Alcoholism, 50% of college students nationwide engage in “binge drinking” behavior, having 5 or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is actually lower than the national proportion. In a commissioned study, 347 students are selected randomly from a list of all students enrolled at the college. Of these 156 admitted to having engaged in binge drinking.

a. What is the sample proportion?

Round to 4 places.

b. What is the standard error of the sample proportion?

Round to 4 places.

c. Give a 95% confidence interval for the true proportion of students who binge drink at her college.

From ____ to ______. Round to 2 places. Do not enter as a percent.

d. State the null and alternative hypotheses.

H0:

Ha:

e. Give the test statistic.

= Round to 3 places.

f. State the p-value for this test.

P-value = Round to 4 places.

g. Do the students at this college binge drink less than students do nationwide? (Significance level of α = 0.10.)

o Yes, because the P-value is less than the level of significance

o Yes, because the P-value is greater than the level of significance

o No, because the P-value is less than the level of significance

o No, because the P-value is greater than the level of significance

4-

The P-value for a test was P = 0.026.

a. Is this significant at the 5% level?

o Maybe

o Yes

o No

b. Is this significant at the 1% level?

o Maybe

o No

o Yes

5-

A significance test was reported in an article said the result was significant at the 1% level. Are such results always, sometimes, or never significant at the 5% level?

• Always.

• Sometimes.

• Never

6-

You wish to test the following claim ( ) at a significance level of .

You believe the population is normally distributed, but you do not know the standard deviation.

Data

74.4

87.8

70.5

79.5

66.1

79.7

94.4

69.6

85.0

76.4

85.3

85.9

81.5

69.1

61.4

92.5

77.1

71.8

78.0

101.6

89.6

81.8

68.5

80.3

98.5

82.9

101.6

98.5

99.4

77.7

88.5

72.6

65.3

95.6

85.9

70.5

76.7

82.1

76.1

101.6

92.9

99.4

85.0

77.1

66.1

Use StatCrunch.

• Copy and paste the data into an empty column in Statcrunch

• Select Stat → T Statistics → One Sample → From data

• Select the column the data is in

• Enter the appropriate null claim and alternative hypothesis.

• Press Compute!

a. What is the test statistic for this sample?

test statistic = Round to 3 decimal places

b. What is the p-value for this sample?

p-value = Use Technology Round to 4 decimal places.

c. The p-value is…

o less than (or equal to)

o greater than

d. This test statistic leads to a decision to…

o reject the null

o accept the null

o fail to reject the null

e. As such, the final conclusion is that…

o There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 78.4.

o There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 78.4.

o The sample data support the claim that the population mean is greater than 78.4.

o There is not sufficient sample evidence to support the claim that the population mean is greater than 78.4.

## Research and statistical information

– A tissue manufacturer that has the fourth-largest market share plans to experiment with a 50 cents-off coupon during November and a “buy one, get one free” coupon during December. The experiment will take place at Target stores in St. Louis and Kansas City. Sales will be recorded by scanners from which mean tissue sales for each store for each month can be computed and interpreted. Construct a valid, simple experiment to assess the cause and effect relationship of the price promotions.

Pick an organization of interest to determine a research question or hypothesis that could be addressed in business research for that organization. Some organizations to consider might be Apple, Google, Netflix, Redbox, or BP. Address the following:

– Provide an overview of the problem you identified.

– What are some research components that could be measured in order to address the research question or hypothesis you identified?

– How might a researcher obtain that information?

– What is an attitude? How does your definition of attitude differ from a business definition of attitude? – Why is it difficult to come to a consensus concerning its definition?

– What are some ways that attitude can be measured? What are the pros and cons of each?

– Which do you think is the most accurate method of measuring attitudes? Why?

Part 1: A manufacturer of MP3 players surveyed 100 retail stores in each of the firm’s sales regions. An analyst noticed that in the South Atlantic region the average retail price was $165 (mean) and the standard deviation was $30. In the Mid-Atlantic region the mean price was $170, with a standard deviation of $15. What do these statistics tell us about these two sales regions?

– Hypotheses are tested by using a click-through sequence in a statistical software package. A generalization about a hypothesis is made by comparing it to a significance level, which is a critical probability associated with a statistical hypothesis test that indicates how likely an inference supporting a difference between an observed value and some statistical expectation is true.

– A researcher is asked to determine whether a sales objective of better than $75,000 per salesperson is possible. A market test is done involving 20 salespeople. What types of information might you receive from this type of study? Explain. How might this data be used in the decision making processes in the business?

– Often, researchers are interested in testing differences in mean scores between groups or in comparing how two groups’ scores are distributed across possible response categories. A variety of bivariate statistical tests can be used in these situations.

Identify what tests of difference are appropriate in the following situations. Justify your responses.

– Average campaign contributions (in dollars) to a marketing campaign for healthy living for men is to be compared to contributions to such a campaign for women.

– Average contributions (in dollars) to campaigns for healthy living for people who are 20-30 years old, 30-40 years old, and 40-60 years old are to be compared to each other.

– Human resource managers and chief executive officers have responded “yes,” “no,” or “not sure” to an attitude question. The HR and CEO responses are to be compared.

– One-half of a sample received an incentive in a mail survey while the other half did not. A comparison of response rates is desired.

– A researcher believes that married men will push the grocery cart when grocery shopping with their wives. How would the hypothesis be tested?

– A manager wishes to compare the job performance of a salesperson before ethics training with the performance of that same salesperson after ethics training.

Discuss:

– In the planning of the research design for a nightclub, what research method would be best the Survey, Experiment, Secondary Data study, or Observation and why. What would be the best research method for a restaurant and why?

– How would you begin the sampling process. Would probability or nonprobobility sampling be the best for nightclub and a restaurant. Explain.

## Two way Analysis of variance

I want to see two methods are the significantly same or not. Each methods has 5 variables are inside. so I would like to see each 5 variables from methods A and B are significantly the same and overall the two methods are significantly same or not. Could you set up the statistically methods(experimental design) (Null hypothesis, t-test, F-test interpretation etc…)

## Hypothesis Testing – 3 hypothesis

I am having trouble defining the 3 hypothesis’ which is the very first step of this case. I realize that I would be using t-distribution for the first hypothesis, but I’m not sure where to go and I believe it is because I don’t follow the way the assignment is worded.

## Research Question: Home Price

Considerable focus will be directed toward hypothesis testing methods, analysis, interpretation, and related SPSS application. In hypothesis testing is to create a testable research hypothesis. This hypothesis will be formalized and written as a null hypothesis (Ho) and an alternative or research hypothesis (Ha). Please see attachments

## SPSS project

Running a test to specifically explain your results could be answered by using a two-tailed hypothesis test. What happens, assuming that you reject the null hypothesis? (Please see attachment).

## How do you perform a t-test?

How is hypothesis testing performed using t-tests?

How do you write out Ho and Ha?

What are the options for determining whether a hypothesis test result is significant?

What are critical regions?

How do you determine which t-test is most appropriate to use?

## One ANOVA Testing

Hi Chris,

The beginning question is asking “In your area of psychology.” My area of psychology is Applied Behavioral Analyst or Behavioral Therapist or Clinical Psychology. This exercise trying to get one ready for research area involving psychological questions that may arise in one career into one the areas involving psychology. Chris you can feel free to use another area in psychology if you prefer, as long as the related content of this posting is related to some form of psychology. If you have any questions please feel free to ask me.

a. ANOVA Testing: In your area of psychology, formulate a research question that can be addressed using a one-way ANOVA test. You may use and expand your research question and include more than two groups to compare. Write down your question and why you feel that it is appropriate for a one-way ANOVA test.

b. State Hypotheses: State your null hypothesis and your alternative hypothesis. State your dependent variable, your independent variable, and the three or more groups that you plan to compare.

c. Describe Data: Describe the type of data you would collect. What sample size would you use and what would your data look like?

d. Predict Results: Predict the results of your ANOVA test and write out the appropriate conclusion. Using alpha of .05, include a pretend p-value (Sig. of your F test) that would justify either accepting or rejecting your null hypothesis. What would you expect from a Post Hoc test given your predicted results from your ANOVA test?

Here is a Helpful Example and Explanations as well as Guidelines for this assignment

In Unit 7, you considered the t-test for independent means, and you used this test to compare two sample groups from the independent variable. In Unit 7, my research question was whether creating video lectures for my students will significantly affect total class points.

In Unit 7, I had a class of 30 students. To research this question, I gave 15 students access to video tutorials each week, and the other 15 did not have access.

My dependent variable was total class points.

My question was whether the mean total class points for Group1 (students WITH video access) was significantly different from Group 2 (students WITHOUT video access).

Ho: mean total points for Group1 = mean total points for Group2

Ha: mean total points for Group1 ≠ mean total points for Group2

We can expand this concept into having an independent variable that is separated into more than two groups.

Suppose that instead of comparing only two means (Group 1 and Group 2), I want to compare three different groups:

Group 1: Watches all videos (1 per week)

Group 2: Watches half of the videos (1 every other week)

Group 3: Watches none of the videos (no access to videos)

Again, my single independent variable is video access. But in this case, it is now separated into three groups (sometimes called levels or classes).

Because I want to compare the mean total points for all three groups, I must use an ANOVA test.

Ho: mean total points Group1 = mean total points Group2 = mean total points Group3

Ha: mean total points Group1 ≠ mean total points Group2 ≠ mean total points Group3

Suppose I pretend that I am going to reject the null hypothesis Ho. This means that at least one of my three video access groups is significantly different than the others. In other words, using alpha is .05, the p-value (Sig of the F test for ANOVA) is less than alpha and I can reject the null.

Next, I can use the Post Hoc to look at a comparison between all three groups. The results of the Post Hoc will help me to determine which groups are significantly different from each other

## Null and alternative hypothesis for testing means of three groups

For the use of a one-way ANOVA there must be more than two means that are being compared. As a result, the following research question is proposed: Does a six week or 12 week self-monitoring program provided to teens between the ages of 13 and 15 diagnosed with ADHD reduce anxiety levels when compared with no intervention?

In order to answer this question, three different groups will be needed: teens between the ages of 13 and 15 diagnosed ADHD provided with the intervention for six weeks, teens between the ages of 13 and 15 diagnosed ADHD provided with the intervention for 12 weeks, and teens between the ages of 13 and 15 diagnosed ADHD provided with no intervention. This question makes many of the same assumptions that are integral to the use of the independent samples t-test. Specifically, the question assumes that the sample sizes will be equal, the variances will be similar, and the dependent value is from a normally distributed population. The principle difference with this research question is that there are three means that must be compared in order to answer the research question. Based on this reality, the one-way analysis of variance provides the most effective tool for determining if there are any statistically significant differences in the population.

My Research Hypothesis: In teens between the ages of 13 and 15 that have been diagnosed with ADHD, a self-monitoring program provided for 12 weeks will help reduce anxiety as measured by the Beck Anxiety Inventory (BAI) compared with teens that receive the intervention for six weeks or do not receive the intervention at all.

Null Hypothesis: A self-monitoring intervention provided for 12 weeks will have no impact on anxiety levels as measured by the BAI for teens between the ages of 13 and 15 diagnosed with ADHD compared with teens that receive the intervention for six weeks or do not receive the intervention at all.

Alternative Hypothesis: There will be a statistically significant difference in anxiety scores on the BAI for teens between the ages of 13 and 15 diagnosed with ADHD who receive either a 12 week or six week self-monitoring program compared with teens that do not receive the intervention.

Question: I am doing a one way ANOVA hypothesis test. In a short version is this the correct way to statistically write my null hypothesis and alternative hypothesis without writing all the words that have in my null and alternative hypothesis?

Ha: μ1 = μ2 = μ3: mean total points Group1 = mean total points Group2 = mean total points Group3

Ha: μ1≠ μ2 ≠ μ3 : mean total points Group1 ≠ mean total points Group2 ≠ mean total points Group3

## Choosing value of alpha levels

Researchers routinely choose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations in which you might accept a higher level (e.g., 0.1)?

## One-Way & Factorial ANOVA using SPSS

Whenever there are two independent variables and each independent variable has multiple groups, the most appropriate statistical test to use to compare these means and interactions is the two-way (factorial) ANOVA.

## SPSS: One way and Two way ANOVA

Please see attachments for full problem description

1. Compare the different Ethnicities of students in the Stat_Grades.sav class to determine if there is a statistically significant difference in the average Final Examination points between the different ethnicities. Be sure to state the hypothesis, state Ho and Ha, include and explain all SPSS results, and write final conclusions for the full results of the test. Include Post Hoc results and the plot. Be sure that your final conclusions are written in common terms for an average person to understand.

2. Extend the hypothesis from number one above. Compare the different ethnicities of students in the Stat_Grades.sav class and the genders to determine if there is a statistically significant difference in the average Final Examination points between the different ethnicities and different genders. Be sure to state the hypothesis, state all Ho and Ha, include and explain all SPSS results, and write final conclusions for the full results of the test. Include Post Hoc results, note any interactions and whether they are significant, and include and explain the plot. Be sure that your final conclusions are written in common terms for an average person to understand.