Psych 205 Test 2

How should you address the results after completing the hypothesis testing with z scores procedure?

"the evidence suggests" since it is possible that the results occurred because of sampling error.

Type II error

- Occurs when you incorrectly fail to reject the null (didn't reject the null) ( said treatment didn't work but it did) - Can only occur when you do not reject the null

Type I error

- Occurs when you incorrectly rejected the null (said treatment worked but is didn't) - It can only occur when you reject the null

When do you say that there was no significant difference

- When you fail to reject the null - The z value is not in the critical region

a = .05 alpha definiton

The .05 cutoff value that is used to identify which z scores are unlikely if the null is true.

Consider the following: z = 1.97, p < .05. What does the "p" in "p < .05" stand for?

The probability that the obtained difference between the sample and the population means occurred by chance or sampling error.

What is the critical region as referred as

The region of rejection (reject the null)

Null Hypothesis

> or < - - (greater than or equal to and less than or equal to)

Research hypothesis symbol

> or < (greater than or less than)

If a z score is not in the critical region you should conclude that

the z score is unlikely and is due to sampling error and if the z score is high or low it will determine the results of the tested theory.

SEM (standard error of the mean) definition

Measures the standard or typical amount of sampling error expected in a given study.

P value is score found in Appendix A after calculated the z for a sample mean

Mhmm

The mean score of 35 students in a statistics class on a standardized Statistics test was 77. The national mean (i.e., μ) and standard deviation (i.e., σ) for the Statistics test was 73 and 8, respectively. Compute the z score for the Statistics test. Is the difference between this class and the national average significant?

- Z = 2.96 - YES! 2.96 > 1.65

Professor Morales examined the data from a smoking session study, and with alpha set to .05, rejected the null hypothesis, t(23) = 1.94, p = .034. She concluded that the program effectively helped people quit smoking. What is the probability that Professor Morales made a Type I error?

.05

3 things about distribution of sample means

1. Distribution has a mean equal to the population mean (mu) 2. The standard deviation is equal to the standard error of the mean (SEMp = sigma/square root of n) a measure of sampling error. 3. The distribution is normal in shape as long as the sample size is at least 30 or the original population has a normal shape. Form Central Limit Theorem Definition

The 4 basic assumptions of hypothesis tests

1. Independence: The independence of data assumption means that each participant's score within a condition is independent of all other participant's scores within the same condition. (only student's test scores no cheating) 2. Appropriate measurement of variables assumption: Means that the independent variable (IV) must identify a group of people who are different from the population in some way and the dependent variable (DV) must be measured on an interval/ratio scale of measurement 3. The normality of distributions: Means that the distribution of sample means for each condition must have a normal shape 4. Homogeneity of variance: Means hat the variances in each condition of the study are similar.

Characteristics of any distribution of sample means (Table)

1. SPREAD: (standard deviation) will always be equal to SEMp=Sigma/square root of n Knowing the SEM tells researchers how much sampling error to expect 2. CENTER: (mean) will always be the populations mean Knowing the mean tells researchers what sample mean to expect 3. SHAPE: will be normal if the original populations shape is normal Knowing the shape is normal enables using a normal unit table and determining the probability of any of a study's possible sample means or SHAPE: will approach normal if the sample size of each sample is sufficiently large (e.g. N >_ 30)

Why is the central limit theorem powerful?

1. Suggests that sales tend to have means similar to the population from which they were drawn. 2. It enables us to compute the typical amount of sampling error any study is likely to generate.

What 2 things contribute to sampling error

1. The standard deviation of the population (sigma) 2. Size of the sample (N) - As sigma increases SEM increases - As sample size (N) increases SEM and sampling error decreases

The average "psychological health" score for college professors in America is μ = 24 on a standardized psychological health survey. A statistics student from Palomar wants to know if professors from Palomar have psychological health scores that are significantly lower than the national average. The student has 36 Palomar professors complete the survey and finds that their mean to be 21 with a standard deviation of 5. Which of the following is the effect size in this analysis?

A. 0.6 Describe the effect: Medium to Large

An honors statistics instructor wanted to know if the mean performance of his 18 students was significantly better than the national average score. The mean score of the 18 students in his statistics class was 75. The national mean (i.e., μ) and standard deviation (i.e., σ) for the Statistics test was 69 and 11, respectively. Use α = .05. What sample mean should you expect if the null hypothesis is true?

A. 69

As N increases, what happens to the critical value (assume that alpha is .05)?

A. It moves closer to 0.

Which of the following accurately describes the critical region?

A. Sample means that are possible, but not likely if the null hypothesis is true.

An honors statistics instructor wanted to know if the mean performance of his 18 students was significantly better than the national average score. The mean score of the 18 students in his statistics class was 75. The national mean (i.e., μ) and standard deviation (i.e., σ) for the Statistics test was 69 and 11, respectively. Use α = .05. Which of the following is the best summary of the results of this study?

A. The mean performance of the students in the honors statistics class (M = 75) was significantly better than the national mean.

Which of the following statements describes a Type II error?

A. concluding that the treatment did not improve test scores when it did improve test scores

In general, the lower the t-value, the ______ the p-value (assume equal df).

A. higher

If you change the sample size from N = 10 to N = 50 does statistical power increase, decrease, or stay the same?

A. increase

In general, the ______ sample size, the closer the shape of the distribution of sample means is to a normal distribution.

A. larger

What should you conclude if you obtain a z score that is in the critical region?

A. reject the null and conclude that the sample mean is significantly different from the population mean

A survey indicates that the average employee at a local company spends μ = $57 on coffee each week. The distribution of spending amounts is approximately normal with a standard deviation of σ = $11. What statistic would you use to determine, what proportion of the population spends more than $70 a week on coffee?

A. z for a single score

The average "psychological health" score for college professors in America is μ = 24 on a standardized psychological health survey. A statistics student from Palomar wants to know if professors from Palomar have psychological health scores that are significantly lower than the national average. The student has 36 Palomar professors complete the survey and finds that their mean to be 21 with a standard deviation of 5. Which of the following values is the critical t- value in this analysis?

B. −1.6896

An honors statistics instructor wanted to know if the mean performance of his 18 students was significantly better than the national average score. The mean score of the 18 students in his statistics class was 75. The national mean (i.e., μ) and standard deviation (i.e., σ) for the Statistics test was 69 and 11, respectively. Use α = .05. Compute the z for this sample mean. Show your work on the worksheet.

B. 2.31 Is the difference significant? Yes!

The central limit theorem describes three important properties of all distributions of sample means of any given sample size. What are the three properties it describes? Select all that apply.

B. Shape C. Central Tendency D. Variability

Which two of the following are the best descriptions of the standard error of the mean? (Choose 2)

B. The typical distance sample means are from the population mean. E. The typical amount of sampling error expected in the study.

Which of the following will help a researcher REDUCE sampling error?

B. increase the sample size

The study with the larger sample size will have ______ statistical power than the study with the smaller sample size.

B. more

The basic structure for both z-tests and t-tests is such that the numerator is ______ and the denominator is ______.

B. the observed difference between means; the difference expected by chance (sampling error)

A reporter wanted to determine if "rookie" officers issue more parking tickets than average. She took a sample of 25 officers and recorded the number of tickets they issued across one week. She compared the mean of the number of tickets issued by these officers to the mean for all of the officers in the city. Which statistic would you use to determine if "rookies" issue more tickets than the average officer?

B. z for a sample mean

The average student studies 25 hr a week with a standard deviation of 2.5. A professor took a sample of 25 students and gave them special training designed to increase their hours of studying. After the special training was complete, the 25 workers studied 27.5 units every hr. What is the probability of randomly sampling 25 students from the general population and their mean study hours being 27.5 or higher? Which statistic should you use to determine the probability of obtaining a sample mean of 27.5 or higher?

B. z for a sample mean

An honors statistics instructor wanted to know if the mean performance of his 18 students was significantly better than the national average score. The mean score of the 18 students in his statistics class was 75. The national mean (i.e., μ) and standard deviation (i.e., σ) for the Statistics test was 69 and 11, respectively. Use α = .05. What is the NULL hypothesis?

B. μ ≤ 69

Statistical Power

Basically when everything is right (rejecting the null when you should)

Always say research suggests

Because findings could be proven wrong therefore making your study and claim false

An honors statistics instructor wanted to know if the mean performance of his 18 students was significantly better than the national average score. The mean score of the 18 students in his statistics class was 75. The national mean (i.e., μ) and standard deviation (i.e., σ) for the Statistics test was 69 and 11, respectively. Use α = .05. What is the INDEPENDENT VARIABLE

C. Honors Class

Which of the following would be the best one-sentence summary of these results in APA style?

C. The psychological health of the Palomar Professors is significantly lower than national average, t(35) = −3.6, p < .05.

In addition to hypothesis testing, researchers compute effect sizes when comparing sample means. Why do researchers compute effect sizes?

C. quantify the size of the difference between the means

d (effect size) measurements

Close to .2 = small effect size Close to .5 = medium effect size Close to .8 = Large effect size and in between scores are referred to as small medium and medium large

An honors statistics instructor wanted to know if the mean performance of his 18 students was significantly better than the national average score. The mean score of the 18 students in his statistics class was 75. The national mean (i.e., μ) and standard deviation (i.e., σ) for the Statistics test was 69 and 11, respectively. Use α = .05. Compute the effect size for this study. Show your work on the worksheet.

D. 0.54

Which of the following defines a Type I error?

D. Rejecting a true null hypothesis

Which of the following statements describes statistical power?

D. concluding that the treatment improved test scores when it did improve test scores

The average "psychological health" score for college professors in America is μ = 24 on a standardized psychological health survey. A statistics student from Palomar wants to know if professors from Palomar have psychological health scores that are significantly lower than the national average. The student has 36 Palomar professors complete the survey and finds that their mean to be 21 with a standard deviation of 5. Which of the following values is the obtained t-value in this analysis?

D. −3.6 Reject the null hypothesis? Yes!

Z for a sample mean

Denominator is SEMp

The average "psychological health" score for college professors in America is μ = 24 on a standardized psychological health survey. A statistics student from Palomar wants to know if professors from Palomar have psychological health scores that are significantly lower than the national average. The student has 36 Palomar professors complete the survey and finds that their mean to be 21 with a standard deviation of 5. Which of the following values would represent the value of sampling error in this analysis?

E. 0.833

The average "psychological health" score for college professors in America is μ = 24 on a standardized "psychological health" survey. A statistics student from Palomar wants to know if professors from Palomar have "psychological health" scores that are significantly lower than the national average. The student has 36 Palomar professors complete the survey and finds that their mean to be 21 with a standard deviation of 5. Which of the following would be the best null hypothesis for this statistical analysis? Do a one-tailed test.

F. the psychological health of the Palomar professors will be 24 or higher

If a z score is not inside the critical region

Fail to reject the null

What does effect size tell us

How many standard deviations a score is above the mean for the population who were not part of the IV group

What does effect size help find?

How much of the results improved or disproved

Where do you find the "probability" of a z score?

In Appendix A

Computing and interpreting the z for a sample mean

Look at Ch. 5 pg. 124-125

d (effect size) formula

M-mu/sigma

A Statistics test has a national mean of μ = 73 and a standard deviation of σ = 8. How much sampling error would you expect for a sample with a size of 100?

SEMs = 0.8

SEM (Standard Error of the Mean) Formula

Sigma (population)/square root of n

Distribution of sample means (Definition)

The population if all possible random sample means for a study conducted with a given sample size

Critical value

The value located at the beginning of unlikely z score area (the shaded area)

Define "Statistical Significance"

There is a low probability that the difference between the sample mean and the population mean occurred due to Sampling error (or random chance).

68-95-99% rule

Used when calculated and measuring how many standard deviations away from the mean a sample or score is.

When do you describe results and statistically significant

Whenever the obtained z value is in the critical region and when you reject the null. It means that the results are unlikely due to sampling error.

Are Z scores with a probability lower than .05 considered unlikely

Yes

Is the research hypothesis always the opposite of the null hypothesis

Yes, if the research hypothesis is trying to prove something then the null hypothesis would try to disprove whatever the research hypothesis is trying to prove.

Should SEM be small

Yes, since it means that there is less sampling error.

What alpha value should you choose if you want to minimize Type I errors?

a of .01 (1%)

What alpha value should you choose if you want to maximize statistical power?

a of .05 (5%)

The incomes of a population of statisticians have a normal distribution with mean US$65,000 and standard deviation US$15,000. Sixty-four statisticians are selected at random from the above population to serve as a sample in a research project. Use the z for a sample mean formula and determine the probability that the one sample of 64 statisticians drawn at random will have a mean salary of US$68,000 or greater?

p = .0548

What does P value mean

probability

If a p value is less than or equal to the alpha value

reject the null and had positive impact on answer

When performing a z for a sample mean

researchers expect the z score to be close to 0 if the null hypothesis is true. If a z score is close to 0 it has high probability than a z score that is far away from the z score. If a probability is low enough the null is rejected.

If the z score is in the critical region then

the P value will be smaller than the alpha value (also indicator of whether or not a null should be rejected)

An honors statistics instructor wanted to know if the mean performance of his 18 students was significantly better than the national average score. The mean score of the 18 students in his statistics class was 75. The national mean (i.e., μ) and standard deviation (i.e., σ) for the Statistics test was 69 and 11, respectively. Use α = .05. What is the RESEARCH hypothesis?

μ > 69

Sampling error is the discrepancy between a sample statistic and a population parameter. Which of the following represents the calculation of sampling error?

σ/√N