Assignment #11 Single Sample t-Test

What factor determines whether you should use a z-test or a t-test statistic for a hypothesis test?

A sample of n = 16 individuals is selected from a population mean of : = 74. A treatment is administered to the individuals in the sample and, after treatment, the sample variance is found to be s2 = 64.

- If the treatment has a 3-point effect and produces a sample mean of M =

77, is this sufficient to conclude that there is a significant treatment effect

using a two-tailed test with ” = .05?

- If the treatment has a 6-point effect and produces a sample mean of M =

80, is this sufficient to conclude that there is a significant treatment effect using a two-tailed test with ” = .05?

A major corporation in the Northeast noted that last year its employees averaged : = 5.8 absences during the winter season (December to February). In an attempt to reduce absences, the company offered free flu shots to all employees this year. For a sample of n = 100 people who took the shots, the average number of absences this winter was M = 3.6 with SS = 396. Do these data indicate a significant decrease in the number of absences? Use a one-tailed test with ” = .05.

On a standardized spatial skills task, normative data reveal that people typically get : = 15 correct solutions. A psychologist tests n = 7 individuals who have brain injuries in the right cerebral hemisphere. For the following data, determine whether or not right-hemisphere damage results in significantly reduced performance on the spatial skills task. Test with alpha (“) set at .05 with one tail. The data are as follows: 12, 16, 9, 8, 10, 17, 10.

11.3

11.4

I. Assumptions for t-test A. Populations

Single Sample t-test

1. the population from which the sample is selected is normal

- One random sample (with replacement)

- Data values

- Sample values known (mean, standard deviation)

- Population values (mean, standard deviation) not known

- Sample values known (mean, standard deviation)
- Diagramming your research (shows the whole logic and process of hypothesis testing)

- Draw a picture of your research design (see diagramming your research handout).

- There are always two explanations (i.e. hypotheses) of your research results, the

wording of which depends on whether the research question is directional (one-tailed)

or non-directional (two-tailed). State them as logical opposites.

- For statistical testing, ignore the alternative hypothesis and focus on the null hypothesis,

since the null hypothesis claims that the research results happened by chance through

sampling error.

- Assuming that the null is true (i.e. that the research results occurred by chance through

sampling error) allows one to do a probability calculation (i.e. all statistical tests are nothing more than calculating the probability of getting your research results by chance through sampling error).

- Observe that there are two outcomes which may occur from the results of the probability calculation (high or low probability of getting your research results by chance, depending on the alpha (α) level).

- Each outcome will lead to a decision about the null hypothesis, whether the null is probably true (i.e. we then accept the null to be true) or probably not true (i.e. we then reject the null as false).

- Draw a picture of your research design (see diagramming your research handout).
- Hypotheses (i.e. the two explanations of your research results)

- Two-tailed (non-directional research question)

- Alternative hypothesis (H1): The independent variable (i.e. the treatment) does make a difference in performance.

- Null hypothesis (H0): The independent variable (i.e. the treatment) does not make a difference in performance.

- Alternative hypothesis (H1): The independent variable (i.e. the treatment) does make a difference in performance.
- One-tailed (directional research question)

- Alternative hypothesis (H1): The treatment has an increased (right tail) or a

decreased (left tail) effect on performance.

- Null hypothesis (H0): The treatment has an opposite effect than expected or no

change in performance.

- Alternative hypothesis (H1): The treatment has an increased (right tail) or a

- Two-tailed (non-directional research question)
- Determine critical regions (i.e. the z score boundary between the high or low probability of getting your research results by chance) using table A-23

A. Significance level (should be given or decided prior to the research; also called the

1

confidence, alpha, or p level)

1. α or p = .05, .01, or .001

- One- or two-tailed test

- One-tailed: use the first row across the top

- Two-tailed: use the second row across the top

- One-tailed: use the first row across the top
- Degrees of freedom

1. df = n – 1

D. With degrees of freedom & one- or two-tailed α value, find the critical t value

- If two-tailed, then critical t value is ± t value

- If one-tailed, then determine if critical t value is +t (right tail; expecting an

increase) or -t (left tail; expecting a decrease)

- Calculate t-test statistic

- General statistical test formula

t = observed sample mean – hypothesized populational mean standard error

- Calculations

- Compute variance

∑????2 − (∑????)2 ????????

s2= ???? or

????−1 ????????

- Compute standard error (average distance between sample & pop means)

Note: (standard error is simply an estimate of the average sampling error which may occur by chance, since a sample can never give a totally accurate picture of a population

√????2 ????

- Compute t-test statistic (i.e. calculates the probability of getting your research results by chance through sampling error)

????−μ ????????

- Compute variance
- Compare the calculated t-score to the critical t-score & make a decision about the null hypothesis

- Reject the null (as false) and accept the alternative or

- Accept null (as true)

- Reject the null (as false) and accept the alternative or

- General statistical test formula
- Reporting the results of a Single Sample t test

“The treatment had a significant effect on (M = 25, SD = 4.22); t(18) = +3.00, p < .05, two-tailed.”

2

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.