Statistics Test #5 - Chapters 9 & 10, unit #4 - stats test, (ACTUAL) - Test #3 - Stats, psych stats quiz 5, psych stats quiz 4, Psyc Stats Quiz 3, Test 3 Quiz - stats, Ch 5 Q's, Ch 6 Questions

Suppose that you sell ice cream from a cart on the street. After you pay the ice cream supplier, the regression line that predicts your ice cream profits from the number of hours you work has a slope of 15. But the man who owns the cart charges you $5 per hour in rent. How much money will you earn per hour?

$10

The formula for calculating the 95% probable limits on an observation is

(μ ± 1.96σ)

Calculate the standard deviation of the following set of data X 22 19 18

2.08

Using the data below, what is the slope when you predict y with x? x y 2.00 7.00 4.00 7.00 6.00 2.00 8.00 2.00

-1

Using the following data, what is the intercept? Round your answer to the nearest 3 decimal places. Please keep your work because the next few questions use this same data. x y 6.00 2.00 7.00 3.00 9.00 7.00 10.00 8.00

-7.8

Using the following data, what would be the value of y when x equals zero? Round your answer to the nearest 1 decimal place. Please keep your work because the next few questions use this same data. x y 6.00 2.00 7.00 3.00 9.00 7.00 10.00 8.00

-7.8

glossary of chapter 7

-Additive law of probability Given a set of mutually exclusive events, the probability of the occurrence of one event or another is equal to the sum of their separate probabilities -Analytic view Definition of probability in terms of an analysis of possible outcomes -Conditional probability The probability that one event will occur given the occurrence of some other event -Density Height of the curve for a given value of X; closely related to the probability of an observation falling in an interval around X -Event The outcome of a trial -Exhaustive A set of events that represents all possible outcomes -Frequentist view Definition of probability in terms of past performance -Independent events Events are independent when the occurrence of one has no effect on the probability of the occurrence of the other - Joint probability The probability of the co-occurrence of two or more events -Multiplicative law of probability The rule giving the probability of the joint occurrence of independent events -Mutually exclusive Two events are mutually exclusive when the occurrence of one precludes the occurrence of the other -Odds The number of occurrences of an event divided by the number of nonoccurrences - Odds ratio The ratio of two odds -Risk The number of occurrences on one event divided by the total number of occurrences of events—a probability -Risk ratio or relative risk The ratio of two risks -Sample with replacement Sampling in which the item drawn on trial N is replaced before the next draw -Subjective probability Definition of probability in terms of personal subjective belief in the likelihood of an outcome -Unconditional probability The probability of one event ignoring the occurrence or nonoccurrence of some other event

i am looking down on a parking lot, and can see that 40% of the vehicles are silver, and about 25% of the vehicles are pickup trucks. Assuming that color and vehicle type are independent, the probability that the next vehicle to leave the parking lot will be a silver pickup is

.10

glossary of chapter 8

-alpha The probability of a Type I error -Alternative hypothesis (H1) The hypothesis that is adopted when H0 is rejected; usually the same as the research hypothesis. -beta The probability of a Type II error - Critical value The value of a test statistic at or beyond which we will reject H0 - Decision making A procedure for making logical decisions on the basis of sample data -Hypothesis testing A process by which decisions are made concerning the value of parameters - Null hypothesis (H0) The statistical hypothesis tested by the statistical procedure; usually a hypothesis of no difference or no relationship. -One-tailed test (directional test) A test that rejects extreme outcomes in one specified tail of the distribution -Power The probability of correctly rejecting a false null hypothesis - Rejection level (significance level) The probability with which we are willing to reject H0 when it is, in fact, correct - Rejection region The set of outcomes of an experiment that will lead to rejection of H0 -Research hypothesis The hypothesis that the experiment was designed to investigate -Sample statistics Statistics calculated from a sample and used primarily to describe a sample. -Sampling distribution of the mean: The distribution of sample means over repeated sampling from one population -Sampling distributions The variability of a statistic over repeated sampling from a specified population -Sampling error Variability of a statistic from sample to sample due to chance -Standard error The standard deviation of a sampling distribution -Test statistics The results of a statistical test. -Two-tailed test (nondirectional test) A test that rejects extreme outcomes in either tail of the distribution -Type I error The error of rejecting when H0 it is true. -Type II error The error of not rejecting when H0 is false

You conduct a study to determine whether the math scores of males and females differ. You use an alpha of .05. What would be the Type I error rate?

.05 Alpha and Type I error are the same.

given a normal distribution of intelligence test scores, what is the probability that someone will score between 100 and 115

.34

What is the probability that we randomly select one person who is a male? Gender Political Party Affiliation Democrat Republican Total Male 25 35 60 Female 35 25 60 Total 60 60 120

.50 or 0.5

In a normally distributed distribution with a mean of 100 and standard deviation of 10, what is the probability that a randomly selected score will fall between 90 and 120? Your answer should be expressed as a probability (e.g. 0.20) and not as a percentage (e.g. 20% or 20 or 20 percent). Please round your answer to the nearest 2 decimal places. You answer should be in the following form... 0.46, for example.

.8185 aka Answer: 0.82

Using the attached SPSS output, what is the p-value that tests the null hypothesis that the relationship between eahtot and wrtot is zero?

0

there are a few z scores that we use often that are worth remembering. the upper 50%, and 97.5 percent of a normal distribution are cut off by z scores of

0.0 and 1.96

There are a few z scores that we use often that are worth remembering. The upper 50%, and 97.5 percent of a normal distribution are cut off by z scores of

0.0, and 1.96

There are a few z scores that we use often that are worth remembering. The upper 50%, and 97.5 percent of a normal distribution are cut off by z scores of:

0.0, and 1.96

What if you had 35 males and 65 females in a class and you put their names on separate pieces of paper and placed them in a bowl. What would be the probability of selecting 5 people from the bowl (one at a time) and all 5 of the people being male? You do not replace names after you drawn them out of the bowl. Round your answer to the nearest 2 decimal places.

0.004 The solution uses the multiplicative law because there are multiple events and we can say what is the probability that the 1st draw is a male AND the 2nd draw is a male AND the 3rd draw is a male AND the 4th person is a male AND the 5th person is a male. The words AND make this the multiplicative law. The probability is ... 35/100 * 34/99 * 33/98 * 32/97 * 31/96 = 0.004311 notice that the denominator of these probabilities are reduced by one each time because we do not replace the names.

If you used an alpha of .01, what is the probability of rejecting a true null hypothesis?

0.01 The probability of rejecting a true null hypothesis is Type I error and it is equal to alpha. If we used an alpha of .01, the probability is .01 (your answer must be entered as .01).

Suppose that you had 100 marbles in bag as described below. If you randomly picked two marble from the bag (with replacement), what would be the probability that the first marble is yellow and the second marble is brown? Do not write your answer as a percentage. For example, if your answer was 20/80, you would write your answer as 0.25, not 25% or 25.0% or 25.00% or 25 as a whole number. Color Quantity Brown 10 Blue 15 Black 27 Yellow 40 Green 8

0.04

The following data are from 10 health-planning districts in Vermont. Y is the percentage of live births less than or equal to 2,500 grams. X1 is the fertility rate for women < 17 or > 35 years of age. X1 is the "high risk fertility rate." What is the unstandardized regression coefficient (i.e. the slope) for X1 when we predict Y with X1? Please round your answer to the nearest 3- decimal places. Please keep your work because the next two questions will use the same data. Y X1 6.1 43.0 7.1 55.3 7.4 48.5 6.3 38.8 6.5 46.2 5.7 39.9 6.6 43.1 8.1 48.5 6.3 40.0 6.9 56.7

0.069

Calculate the variance of the following set of data. X 20 16 12

The variance is 16 and the standard deviation is 4.00.

In a normally distributed distribution with a mean of 100 and standard deviation of 12, what is the probability that a randomly selected score will fall between 88 and 76? Your answer should be expressed as a probabilty (e.g. .20) and not as a percentage (e.g. 20% or 20 or 20 percent). Please round your answer to the nearest 4 decimal places. You answer should be in the following format ... 0.2543, for example.

0.1359 88 is 1 SD below the mean and 76 is 2 SDs below the mean. So, you take the area from mean to z of 2 SD and subtract from that the area from mean to z for 1. = .4772 - .3413 = .1359

If the power in your study is .80, what is beta?

0.20 Power is 1 - beta. So, if power is .80, beta is .20.

What is the probability that we randomly pick a person who is a male democrat? Round your answer to the nearest 2 decimal places. Gender Political Party Affiliation Democrat Republican Total Male 25 35 60 Female 35 25 60 Total 60 60 120

0.21

Suppose you are a doctor in the emergency room and you are seeing a patient who was involved in a motorcycle accident. There is reason to believe the patient has brain damage. You give the patient a finger-tapping speed test that has a mean of 80 and standard deviation of 5 in the healthy population. You use a one tailed test, with the rejection region on the left hand side of the distribution and you use an alpha of 0.05. If you believed the unhealthy population of people with brain damage has a mean of 70 and standard deviation of 5 on the test, what would be the power of the study you conduct on patients who come into the emergency room with possible head injuries? Round your answer to the nearest 2 decimal places. Attached file is the solution.

0.36 The null hypothesis testing situation will reject a score below 71.775. That is the point at which 5% of the distribution with a mean of 80 and standard deviation of 5 would fall below. This is obtained by ... a) using the z-score where 5% of the distribution falls below and multiplying it by the standard deviation of 5. = 1.645 * 5 = 8.225 b) subtract this from the mean to get X = 80 - 8.225 = 71.775 Now, we find the z-score for 71.775 in the alternative distribution of unhealthy people.. = (71.755 - 70) / 5 = 0.355 The larger portion of the z-table, for a z-score of 0.355 is the Type II error of the study. It is approximately 0.64. I took a value between a z of .35 (.6368) and a z of .36 (.6406). The smaller portion of the table is power, which would be .36. Power = 1- Type II error This is a pretty complicated scenario to follow. A few videos discuss this. It is most closely discussed in the video called "Type 1 and Type 2 errors and the area under the curve, using R and Excel".

The data show how many young (below 25 years old) and older people (over 40 years old) can run an 8 minute mile, in a sample of 150. What is the probability that a randomly selected person can run an 8 minute mile, given the fact that he/she is an older person? Age Group Can run an 8 minute mile Yes No Total Young 50 20 70 Older 35 60 95 Total 85 80 165

0.37

Suppose that you had 100 marbles in bag as described below. If you randomly picked one marble from the bag, what would be the probability that the marble is yellow? Do not write your answer as a percentage. For example, if your answer was 20/80, you would write your answer as 0.25, not 25% or 25.0% or 25.00% or 25 as a whole number. Color Quantity Brown 10 Blue 15 Black 27 Yellow 40 Green 8

0.40

What is the risk that an older person can run an 8 minute mile? Age Group Can run an 8 minute mile Yes No Total Young 50 20 70 Older 35 45 80 Total 85 65 150

0.44 The risk that an older person can run an 8 minute mile is 35 / 80 = 0.4375 or 0.44 rounded.

Using the following data, what is the standard error of the estimate? Round your answer to the nearest 3 decimal places. Please keep your work because the next few questions use this same data. x y 6.00 2.00 7.00 3.00 9.00 7.00 10.00 8.00

0.447

Using the attached SPSS output, what is the correlation between eahtot and itn?

0.476

What is the obtained chi-square of the following 2 x 2 contingency table? Success Relapse Total Drug: 35.000 16.000 51.000 Placebo: 12.000 8.000 20.000

0.478 or 0.48

Using the following data, what would be beta? Round your answer to the nearest 3 decimal places. Please keep your work because the next few questions use this same data. x y 6.00 2.00 7.00 3.00 9.00 7.00 10.00 8.00

0.992

Suppose that you had 100 marbles in bag as described below. If you randomly picked one marble from the bag, what would be the probability that the marble is either yellow or brown? Do not write your answer as a percentage. For example, if your answer was 20/80, you would write your answer as 0.25, not 25% or 25.0% or 25.00% or 25 as a whole number. Color Quantity Brown 10 Blue 15 Black 27 Yellow 40 Green 8

0.5

What is the probability that we randomly select one person who is a democrat? Gender Political Party Affiliation Democrat Republican Total Male 25 35 60 Female 35 25 60 Total 60 60 120

0.50

The data show how many male and female adults, in a sample of 120 adults, are affiliated with the democratic party and the republican party. What is the odds ratio? Gender Political Party Affiliation Democrat Republican Total Male 25 35 60 Female 35 25 60 Total 60 60 120

0.51

What is the probability that a randomly selected person will be a republican, given the fact that he is a male? Gender Political Party Affiliation Democrat Republican Total Male 25 35 60 Female 35 25 60 Total 60 60 120

0.58 This is a conditional probability and we know this by the word "Given" in the question. When we say "given that he is a male" we are only concerned with males. We totally ignore females. Out of 60 males, there were 35 males who were Republicans. The probability = 35 / 60 = 0.58

This is the same scenario as the previous question, but a different question. Suppose you are a doctor in the emergency room and you are seeing a patient who was involved in a motorcycle accident. There is reason to believe the patient has brain damage. You give the patient a finger-tapping speed test that has a mean of 80 and standard deviation of 5 in the healthy population. You use a one tailed test, with the rejection region on the left hand side of the distribution and you use an alpha of 0.05. If you believed the unhealthy population of people with brain damage has a mean of 70 and standard deviation of 5 on the test, what would be type II error for the study you conduct on patients who come into the emergency room with possible head injuries? Round your answer to the nearest 2 decimal places.

0.64 Type 2 error is 1 - power. We would follow all the same procedures above, but we would look at the larger portion of our final z-score to find type II error, instead of the larger portion of the z-score that we used to find power. The larger portion of the z-table, for a z-score of 0.355 is the Type II error of the study. It is approximately 0.64. I took a value between a z of .35 (.6368) and a z of .36 (.6406). The smaller portion of the table is power, which would be .36. Power = 1- Type II error This is a pretty complicated scenario to follow. A few videos discuss this. It is most closely discussed in the video called "Type 1 and Type 2 errors and the area under the curve, using R and Excel". The null hypothesis testing situation will reject a score below 71.775. That is the point at which 5% of the distribution with a mean of 80 and standard deviation of 5 would fall below. This is obtained by ... a) using the z-score where 5% of the distribution falls below and multiplying it by the standard deviation of 5. = 1.645 * 5 = 8.225 b) subtract this from the mean to get X = 80 - 8.225 = 71.775 Now, we find the z-score for 71.775 in the alternative distribution of unhealthy people.. = (71.755 - 70) / 5 = 0.355 The smaller portion of the z-table, for a z-score of 0.355 is the type 2 error (Beta) of the study. This is a pretty complicated scenario to follow. A few videos discuss this. It is most closely discussed in the video called "Type 1 and Type 2 errors and the area under the curve, using R and Excel".

If Type II error equals .30, what is power?

0.70 Power is 1 - Beta. So, if beta equals .30, power equals .70.

What is the risk ratio? Round your answer to the nearest 2 decimal places.

0.71 RR = 25*60 / 35*60 = .714 = .71

What are the odds that an older person can run an 8 minute mile? Age Group Can run an 8 minute mile Yes No Total Young 50 20 70 Older 35 45 80 Total 85 65 150

0.78 Odds that an older person can run an 8 minute mile is 35 / 45 = 0.7778 or 0.78 rounded.

In a normally distributed distribution with a mean of 80 and standard deviation of 12, what is the probability that a randomly selected score will fall below 92? Your answer should be expressed as a probabilty (e.g. .20) and not as a percentage (e.g. 20% or 20 or 20 percent). Please round your answer to the nearest 5 decimal places.

0.8413 bc it is larger portion

If you used an alpha of .05, what would be the probability of failing to reject the null hypothesis when the null is true? Note: When answering questions about probabilities, your answer should be equal to or less than 1.00 (e.g. .25, .05, .95, .50 etc.). Be sure to include the decimal point.

0.95. The probability of failing to reject a true null hypothesis is a correct decision with the probability of 1 - alpha. If alpha is .05, then the probabilty is 1-.05 = .95.

Using the following data, what would be the Pearson Product Moment Correlation (ususally simply referred to as the correlation)? Round your answer to the nearest 3 decimal places. x y 6.00 2.00 7.00 3.00 9.00 7.00 10.00 8.00

0.992

Given the numbers 1, 2, and 3, the standard deviation is

1

Using the data below, what is the slope when you predict y with x? x y 2.00 2.00 4.00 2.00 6.00 7.00 8.00 7.00

1

A z score of -1.50 represents an observation that is:

1 1/2 standard deviations below the mean.

If your were testing the null hypothesis that Germany, Switzerland and the United States had the same average scores on a happiness score, which statistic would you use? Happiness is a quantitative (continuously measured) variable.

1-way ANOVA

The standard deviation for the numbers 8, 9, and 10 is:

1.0

Given the following distribution, what would be the mean of the transformed distribution if you created a new distribution by dividing each number in the distribution by 5? X 2 4 7 8 10

1.24

A z score of 1.25 represents an observation that is:

1.25 standard deviations above the mean

a z score of 1.25 represents an observation that is

1.25 standard deviations above the mean

What are the odds that a female will be a democrat?

1.4 The odds that a female will be a democrat = 35 / 25 = 1.40

Using the following data, what is the slope? Round your answer to the nearest 3 decimal places. Please keep your work because the next few questions use this same data. x y 6.00 2.00 7.00 3.00 9.00 7.00 10.00 8.00

1.6

What is the ratio? Age Group Can run an 8 minute mile Yes No Total Young 50 20 70 Older 35 45 80 Total 85 65 150

1.63 The risk that a young person can run an 8 minute mile is 50 / 70 = 0.714286 The risk that an older person can run an 8 minute mile is 35 / 80 = 0.4375 The risk ratio is 0.714286 / 0.4375 = 1.63

a test score of 84 was transferred into a standard score of -1.5. if the mean of test scores was 99, what is the standard deviation of the test scores

10

If you had a standard deviation of 10, what would be the variance?

100

Suppose that your study investigated the effect of balance on hip fractures in nursing homes. Out of 225 individuals with good balance, 25 had hip fractures. Among those with poor balance 10 had a hip fracture and 210 did not. In the 2x2 table, put good balance and hip fracture in cell A and poor balance and no hip fracture in cell D. What is the risk (a.k.a. incidence rate) of people who have good balance ? Express your answer as the rate per 100 people.

11.11 or 11.11%

If your sample had a variance of 144, what would be the standard deviation?

12

Using the attached SPSS output, what is the sample size?

140

Suppose that you had a population that consisted of the numbers 1, 2, 3, 4 and 5. What would be the long run average variance of the sample variances drawn from the population using n-1 in the denominator of the sample variance? Suppose that your samples were all sample size of 5. Round your answer to the nearest 2 decimal places.

2

Suppose that your study investigated the effect of balance on hip fractures in nursing homes. Out of 225 individuals with good balance, 25 had hip fractures. Among those with poor balance 10 had a hip fracture and 210 did not. In the 2x2 table, put good balance and hip fracture in cell A and poor balance and no hip fracture in cell D. What is the risk ratio for this study _____ (round your answer to the nearest 2 decimal points)?

2.44

Suppose that your study investigated the effect of balance on hip fractures in nursing homes. Out of 225 individuals with good balance, 25 had hip fractures. Among those with poor balance 10 had a hip fracture and 210 did not. In the 2x2 table, put good balance and hip fracture in cell A and poor balance and no hip fracture in cell D. What is the odds ratio for this study _____ (round your answer to the nearest 2 decimal points)?

2.63

We know that 25% of the class got an A on the last exam, and 30% got a B. What percent got either an A or a B?

25% + 30% = 55%

If the correlation is .50, what percent of variance in y is explained by x? Please include two decimal points in your answer.

25.00 r-square (the coefficient of determination) tells us the proportion of variance in one variable that is explained by the other variable. The square of .50 is .25 and multiplying .25 by 100 tells us the percent of variance in y that is explained by x.

if the standard deviation of the population is 15 and we repeatedly draw a sample of 25 observations each: the resulting sample means we will have a standard error of

3

The data show how many young (below 25 years old) and older people (over 40 years old) can run an 8 minute mile, in a sample of 150. What is the odds ratio? Age Group Can run an 8 minute mile Yes No Total Young 50 20 70 Older 35 45 80 Total 85 65 150

3.21 Odds that a young person can run an 8 minute mile = 50 / 20 = 2.5 Odds that an older person can run an 8 minute mile = 35 / 45 = 0.777778 OR = 2.5 / 0.77778 = 3.214, rounded to the nearest 2 decimal places is 3.21

The following data are from 10 health-planning districts in Vermont. Y is the percentage of live births less than or equal to 2,500 grams. X1 is the fertility rate for women < 17 or > 35 years of age. X1 is the "high risk fertility rate." What is the intercept in the regression analysis that uses X1 to predict Y? Please round your answer to the nearest 2 decimal places. Please keep your work because the next question will use the same data. Y X1 6.1 43.0 7.1 55.3 7.4 48.5 6.3 38.8 6.5 46.2 5.7 39.9 6.6 43.1 8.1 48.5 6.3 40.0 6.9 56.7

3.53

If we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expect that 95% of our observations would lie in the interval that is approximately

30-70

if we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expect that 95% of our observations would lie in the interval that is approximately

30-70

A data set of intelligence scores was collected from high school seniors. The IQ scores ranged from 82 to 113. Which of the following is probably NOT a reasonable estimate of the standard deviation?

35.4

of 50 women treated for breast cancer in the local cancer unit, 35 of them survived for at least 5 years. For a woman who has just been diagnosed with breast cancer, our best guess is that the probability that she will survive for 5 years is

35/50= .70

if we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expect that 68% of our observations would lie in the interval that is approximately

40-60

Given the following data, what is the raw data covariance between x and y? Round your answer to the nearest 2 decimal places. x y 12 15 10 17 8 10

5

last year there were 300 new Ph.Ds in chemistry looking for academic jobs. of those 100 were men and 200 were women. nationwide last year there were 75 new hirings in chemistry departments. how many of those new hires would be expected to be women

50

If we have data that have been sampled from a population that is normally distributed with a mean of 60 and a standard deviation of 10, we would expect that 95% of our observations would lie in the interval that is approximately:

50-70

we know that 25% of the class got an A on the last exam, and 30% got a B. what percent got either an a or b

55%

If a correlation is .25, what percent of variance in y can be explained by x? Please include 2 decimal points in your answer.

6.25 squaring .25 equals .0625, multiplying by 100 tells us that 6.25% of the variance in y is explained by x.

In a normally distributed distribution with a mean of 70 and standard deviation of 5, what is the probability that a randomly selected score will fall between 67.75 and 72.25? Your answer should be expressed as a probabilty (e.g. .20) and not as a percentage (e.g. 20% or 20 or 20 percent). Please round your answer to the nearest 3 decimal places. You answer should be in the following format of 0.254, for example.

67.75 is 1/2 SD below the mean and 72.25 is 1/2 SDs above the mean. So, you take the area from mean to z of 1/2 SD and multiply it by 2 because the mean to z of 1/2 SD below the mean is the same as the mean to z of 1/2 SD above the mean (the distribution is symetrical). = .1915 + .1915 = .383 Answer: 0.383

A professor collects data in his class in order to better understand what predicts grades in his class. The professor believes that one of the best predictors of grades is the amount of time students spend studying.The following data resulted in an unstandardized regression coefficient of 0.645776567. What t-obtained value would tell the professor if the slope is significant? Round your answer to the nearest 2 decimal places. Time Studying Grade 22 68 44 82 35 78

7.2

A clinic wants to identify patients who score low on a test so that the patients can be offered a new therapy. The scores are normally distributed distributed with a mean of 80 and standard deviation of 12. The clinic decides to find the lowest 40% of scores. What is the score that marks the 40th percentile? Round your answer to the nearest 2 decimal places.

76.94

A test score of 84 was transformed into a standard score of -1.5. If the standard deviation of test scores was 4, what is the mean of the test scores?

90

a test score of 84 was transformed into a standard score of -1.5. if the standard deviation of test scores was 4, what is the mean of the test scores

90

A test score of 84 was transformed into a z score of -1.0. If the standard deviation of test scores was 8, what is the mean of the test scores?

92

In a normally distributed distribution with a mean of 100 and standard deviation of 10, what is the probability that a randomly selected score will fall between 95 and 105? Your answer should be expressed as a probability (e.g. 0.20) and not as a percentage (e.g. 20% or 20 or 20 percent). Please round your answer to the nearest 2 decimal places. You answer should be in the following form... 0.46, for example.

95 is 0.5 SDs below the mean and 105 is 0.5 SD above the mean. Mean to z of 0.5 SD = .1915 So, .1915 + .1915 = .0.383 or 0.38 Answer: 0.38

the text discussed setting "probable limits" on observation's value. these limits are those which have a

95% chance of enclosing the value

in a normal distribution, about how much of the distribution lies within two standard deviations of the mean

95% of the distribution

which of the following is likely to represent a statement of the null hypothesis

= 0

On average, what value is expected for the t statistic when the null hypothesis is true? A. 0 B. 1 C. 1.96 D. Can't be determined without additional information.

A

The estimated standard error, s(M1-M2) in the t-test for independent samples ________________. A. is computed based on the variances, s2 of both samples B. is computed based on the variance, s2 of a larger sample C. is computed based on the variance, s2 of the smaller sample D. is computed based on the population variances, σ2

A

What is the average value expected for the independent-measures t statistic if the null hypothesis is true (i.e., the two samples represent the same population)? A. t = 0 B. t > 1 C. t = 1 D. Can't be determined without more information

A

Which of the following is the correct null hypothesis for an independent samples t-test (assume 2-tails test)? A. There is no difference between populations represented by two samples (i.e., μ1 - μ2 = 0 or μ1 = μ2). B. There is a difference between populations represented by two samples (i.e., μ1 - μ2 ≠ 0 or μ1 ≠ μ2). C. There is no difference between two samples (i.e., M1 - M2 = 0 or M1 = M2 ). D. None of the above.

A

clinical significance

A statististically significant result that is clinically useful

a type I error concerns

the probability of rejecting a true null hypothesis

If we know that the probability for z > 1.5 is .067, then we can say that:

ALL-the probability of exceeding the mean by more than 1.5 standard deviations is .067. b. 86.6% of the scores are less than 1.5 standard deviations from the mean. d. the probability of being more than 1.5 standard deviations away from the mean is .134

Given the 1-way chi-square example above, what would be your conclusion regarding the null hypothesis? In your answer, explain how you came up with your conclusion.

An obtained chi-square of 11.03 is larger than the c.v. of 5.99 so we reject the null hypothesis.

Which of the following statements is true about a negative correlation a. It is not significant b. It is not as important as positive relationships c. As one variable increases, the other variable decreases d. As one variable decreases, the other variable decreases.

As one variable increases, the other variable decreases A negative correlation means that as one variable increases, the other variable will decrease.

For which of the following situations would a repeated-measures research design be appropriate? A. Comparing mathematical skills for girls versus boys at age 10. B. Comparing patients' pain tolerance at the beginning and at the end of physical therapy sessions. C. Comparing self-esteem for students who participate in school athletics versus those who do not. D. Comparing verbal skills of science majors versus art majors at a college.

B

What value is estimated with a confidence interval using the t statistic? A. The value for an unknown sample mean B. The value for an unknown population mean C. The difference between two population means D. The difference between two sample means

B

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution? A. It is almost perfectly normal. B. It is flatter and more spread out than the normal distribution. C. It is taller and narrower than the normal distribution. D. There is no consistent relationship between the t distribution and the normal distribution.

B

Which of the following is a fundamental difference between the t statistic and a z-score? A. The t statistic uses the sample mean in place of the population mean. B. The t statistic uses the sample variance in place of the population variance. C. The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n. D. All of these are differences between t and z.

B

f other factors are held constant, what is the effect of increasing the sample variance? A. It will increase the estimated standard error and increase the likelihood of rejecting H0. B. It will increase the estimated standard error and decrease the likelihood of rejecting H0. C. It will decrease the estimated standard error and increase the likelihood of rejecting H0. D. It will decrease the estimated standard error and decrease the likelihood of rejecting H0.

B

If other factors are held constant, what is the effect of increasing the sample size? A. It will increase the estimated standard error and increase the likelihood of rejecting H0. B. It will increase the estimated standard error and decrease the likelihood of rejecting H0. C. It will decrease the estimated standard error and increase the likelihood of rejecting H0. D. It will decrease the estimated standard error and decrease the likelihood of rejecting H0.

C

In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition. One of the major concerns in this type of study is that participation in the first treatment may influence the participant's score in the second treatment. What is this problem is called? A. Individual differences problem. B. Homogeneity of variance problem. C. Order effect. D. Bi-treatment effect.

C

Which of the following research situations would be most likely to use a between-subjects research design? A. Examining academic performance of the Texas State University students by comparing their mean GPA to the national average GPA of undergraduate population in the U.S.. B. Investigating the long-term effectiveness of a stop-smoking treatment by comparing participants craving for cigarettes after 2 months and 6 months of treatment. C. Examining gender differences in analytical problem solving skills among undergraduate students. D. All of the above.

C

ch. 9 glossary

Correlation Measure of the relationship between variables Correlation coefficient A measure of the relationship between variables Covariance A statistic representing the degree to which two variables vary together Criterion variable The variable to be predicted Curvilinear relationship- A situation that is best represented by something other than a straight line Deviation score- Data in which the mean has been subtracted from each observation Dichotomous variables- Variables that can have only two different values Heterogeneous sub-samples Data in which the sample of observations could be subdivided into two distinct sets on the basis of some other variable Inter-correlation matrix A matrix (table) showing the pairwise correlations among all variables Linear relationship A situation in which the best-fitting regression line is a straight line Monotonic relationship A relationship represented by a line that is continually increasing (or decreasing), but perhaps not in a straight line. Negative relationship A relationship in which increases in one variable are associated with decreases in the other Pearson product-moment correlation coefficient r The most common correlation coefficient Phi The correlation coefficient when both of the variables are measured as dichotomies Point bi-serial correlation (rpb) The correlation coefficient when one of the variables is measured as a dichotomy Population correlation coefficient rho (r) The correlation coefficient for the population Predictor variable The variable from which a prediction is made Range restrictions Cases wherein the range over which X or Y varies is artificially limited Ranked data Data for which the observations have been replaced by their numerical ranks from lowest to highest Regression lines The "line of best fit" that represents a straight line drawn through the data points Scatter plot (scatter diagram, scattergram) A figure in which the individual data points are plotted in two-dimensional space Spearman's correlation coefficient for ranked data (rS) A correlation coefficient on ranked data

For which of the following situations would a repeated-measures design have the maximum advantage over an independent-measures design? A. When many subjects are available and individual differences are small. B. When very few subjects are available and individual differences are small. C. When many subjects are available and individual differences are large. D. When very few subjects are available and individual differences are large.

D

The range of correlations are from -1.00 to +1.00.

true

The t-test for independent sample can be used to examine ____________. A. the mean difference between two treatment conditions in an experiment (e.g. a difference in performance of experimental group and control group). B. the mean difference between two populations in quasi-experimental designs (e.g., mean difference in attitudes to abortion between residents of the southern vs. northern states in the U.S.). C. the mean difference in stress level at the beginning and the end of semester in a sample of undergraduate students. D. A & B E. All of the above.

D

What is indicated by a large variance for a sample of difference scores (i.e., a large variance of D scores)? A. A consistent treatment effect and a high likelihood of a significant difference. B. A consistent treatment effect and a low likelihood of a significant difference. C. An inconsistent treatment effect and a high likelihood of a significant difference. D. An inconsistent treatment effect and a low likelihood of a significant difference

D

ch. 10 Glossary

Errors of prediction- The difference between Y and Y^Least squares regression Refers to the fact that our calculation of the regression line is based on minimizing the squared differences between Y and Y^Regression coefficients The general name given to the slope and the intercept; often refers only to the slope Regression equation The equation that predicts Y from X Regression to the mean The tendency for predicted values to be less extreme (closer to the mean) than the scores from which they are predicted. Residual The difference between the obtained and predicted values of Y Residual variance (error variance)The square of the standard error of estimate Standard error of estimate The average of the squared deviations about the regression line Standardized regression coefficient, beta The regression coefficient that results from data that have been standardized

If you wanted to test the significance of the difference between Germany, Switzerland and the United States happiness scores, which statistic would you use?

F-test

Suppose your study uses a one-tailed test, with the rejection region on the left-hand side of the distribution. You use an alpha of .01, your t-critical value is -1.65 and you obtain a t-statistic of -1.60. What would you conclude?

Fail to reject the null hypothesis With a one-tailed test, there is a rejection region on the left side (negative side) of the distribution. With a critical value of -1.65, -1.60 is not in the rejection region and we fail to reject the null hypothesis.

What would we conclude if we conducted a t-test in which we were willing to make a Type I error 1% of the time and we found a p-value of .02?

Fail to reject the null hypothesis A p-value of .02 means that there is a 2% chance that we would obtain a test statistics of the magnitude that we obtained, if the null hypothesis is true. Unfortunately, if alpha is .01, we are only willing to make a mistake 1% of the time. Therefore, we fail to reject the null hypothesis.

How would you interpret the slope of question #2 above? The answer to this question should be a sentence.

For every unit increase in x, we predict a 1.00 unit increase in y. When a test questions asks to "interpret" a statistic, the question is asking for an answer like this. The answer should be a sentence that is correctly expressed. The word "interpret" has a special meaning in this class. You will be asked to interpret several statistics before the semester is over. In every case, the correct way to interpret a statistic is very important so please pay special attention to interpretations in this class.

when we are using a two-tailed hypothesis test: the null hypothesis is of the form

H0: u = 50

when we are using a two-tailed test: the alternative hypothesis is of the form

H1: u =/ 50

alternative hypothesis

Usually the relationship or difference that the researcher believes to be present

Using the same research scenario above, what would you conclude about the t-obtained value that you calculated? In your answer, please indicate whether you reject the null hypothesis or not, whether the slope is significantly different than zero and fully explain how you came up with your conclusion (base your conclusion on numbers)..

I would fail to reject the null hypothesis because my t-obtained of 7.20 is less than the t-critical value of 12.06. This means that the slope is not significantly different than zero and there is not a relationship between the two variables.

when you are using a one-sample t test: the degrees of freedom are

N - 1

Type I error (alpha)

Occurs when you incorrectly reject the null hypothesis

What would we conclude if we conducted a t-test in which we were willing to make a Type I error 5% of the time and we found a p-value of .02?

Reject the null hypotheses A p-value of .02 means that there is a 2% chance that we would obtain a test statistics of the magnitude that we obtained, if the null hypothesis is true. Unfortunately, if alpha is .01, we are only willing to make a mistake 1% of the time. Therefore, we fail to reject the null hypothesis.

Suppose your study uses an alpha of .01, your t-critical value is 1.65 and you obtain a t-statistic of -1.70. We always assume that we are using a two-tailed test, unless specified otherwise What would you conclude?

Reject the null hypothesis

You are conducting a study to determine whether there is an association between vigorous exercise and strokes and you use an alpha of .05. The t-critical value is 1.96 and you obtain a t-statistic of 2.45. What would you conclude?

Reject the null hypothesis If the t-statistic that you obtain is higher than the t-critical value, you reject the null hypothesis

When we transform scores to a distribution that has a mean of 50 and a standard deviation of 10, those scores are called

T scores

If you wanted to test the significance of a correlation, which statistic would you use?

T-test

null hypothesis

That there is no difference or relationship between variables that is any greater or less than would be expected by chance.

If I reject the null hypothesis, what am I concluding?

The evidence suggests that there is a difference or relationship in my study.

If I reject the null hypothesis, what am I concluding?

The evidence suggests that there is a difference or relationship in my study. The null hypothesis is that there is not a difference or relationship in the population. If we reject the Ho, we are saying that the evidence suggests that there is a difference or relationship in the population.

If I fail to reject the null hypothesis, what am I concluding?

The evidence suggests that there is not a difference or relationship in the study. The null hypothesis is that there is not a difference or relationship in the population. If we fail to reject the Ho, we are saying that we do not have evidence to suggest that there is a difference or relationship in the population.

Which of the following sets of data is likely to have the smallest standard deviation

The grade point averages of students from your high school's honors biology class.

Which of the following would happen if we added a constant to each value in a distribution?

The mean and of the distribution would increase by the same amount of the constant and the variance would remain the same.

Which of the following would take place if we multiplied every score in a distribution by a constant?

The mean of the distribution would increase so that the new mean equals the old mean times the constant and the variance would increase.

true The null hypothesis cannot be proven. That is why we never say "accept the null hypothesis". Instead, we say "fail to reject the null hypothesis".

The null hypothesis cannot be proven, it can only be disproven.

Based on the previous question about a 2 x 2 chi square analysis (see table below), what would you conclude about the null hypothesis? Yes No Drug 35 16 Placebo 12 8

The obtained chi square of 0.48 is lower than the critical value of 3.84 so we fail to reject the null hypothesis. it is the 47th percintile significance level - .05 row totals 51 and 20 - grand total 71 column 47 & 24 p value is .489386 the result is not significant at p less than .05 chi square stat is 0.4779 35 (33.76, 0.05) 12 (13.24, 0.12) 16 (17.24, 0.09) 8 (6.76, 0.23)

Interpret the odds ratio as we have in class.

The odds that a male will be a democrat is .51 times the odds that a female will be a democrat.

The data show how many young (below 25 years old) and older people (over 40 years old) can run an 8 minute mile, in a sample of 150. Interpret the odds ratio? Age Group Can run an 8 minute mile Yes No Total Young 50 20 70 Older 35 45 80 Total 85 65 150

The odds that a young person can run an 8 minute mile is 3.21 times higher than the odds that an older person can run an 8 minute mile.

alpha

The probability of falsely rejecting the null hypothesis

The data show how many young (below 25 years old) and older people (over 40 years old) can run an 8 minute mile, in a sample of 150. Interpret the risk ratio? Age Group Can run an 8 minute mile Yes No Total Young 50 20 70 Older 35 45 80 Total 85 65 150

The risk that a young person can run an 8 minute mile is 1.63 times higher than the risk that an older person can run an 8 minute mile. Note that being able to run an 8 minute mile is considered a good thing so this is not a good example of risk. We could have switched the columns in this table so that not being able to run an 8 minute mile is in the first column. In that case, the risk would be the risk that someone could not run an 8 minute mile. That makes more sense. Below, I have worked out what happens when you switch the columns in the table. The way you set up a table makes a big difference in what the risk ratio and odds ratio tells you. Risk that a young person cannot run an 8 minute mile = 20 / 70 = 0.2857 Risk that an older person cannot run an 8 minute mile = 45 / 80 = 0.5625 Risk ratio = 0.2857 / 0.5625 = 0.5078 The risk that a young person cannot run an 8 minute mile is 0.5078 times the risk that an older person cannot run an 8 minute mile. That is about half the risk of an older person. This is very different than the 1.63 risk ratio that we had when the columns were set up with yes in the first column and no in the second column.

If your study had a power of .80, which of the following statements would be correct?

There is an 80% chance of finding a relationship or difference that actually exists in the real world.

A clinic wants to identify patients who score high on a test so that the patients can be offered a new therapy. The scores are normally distributed with a mean of 90 and standard deviation of 10. The clinic decides to find the highest 2 1/2 % of scores. What is the score that marks the 97.5 th percentile? Round your answer to the nearest 2 decimal places.

To find the score that marks the 97.5 th percentile, you need to find the z-score that is associated with .025 smaller portion of the area under the curve. To find the z above, go down the smaller portion column in the z-table and find the closest z score to a smaller portion of .025. That z-score will be the familiar 1.96. Because the 97.5 th percentile is above the mean, you add this to the mean in the following formula... So, X = 90 + 1.96(10) = 90 + 19.6 = 109.6 answer: 109.6

Which of the following is not a step in hypothesis testing?

Try to make your results agree with other similar studies Researchers typically work within strict ethical guidelines. Study results should always be reported exactly the way they turn out. Besides it being unethical to alter study findings, researchers could easily face serious consequences for tampering with study results--including ruining their carreer.

statistical significance

When the difference you observe between two samples is large enough that it is not simply due to chanceTy

fail to reject the null hypothesis

When you do not have enough statistical strength to show a difference or association

reject the null hypothesis

When you have enough statistical strength to show a difference or association.

You would obtain a negative value for the variance if:

You would never obtain a negative variance

if i am interested in the probability that you will be depressed if you have experienced a great deal of stress in the past month, i am talking about

a conditional probability

The normal distribution is

a distribution with a known shape and other properties

A correlation between .30 and .50 is generally considered ... a. a moderate relationship b. a weak relationship c. a strong relationship d. an insignificant relationship

a moderate relationship According to Jacob Cohen, a moderate relationship is between .30 and .50.

all of the following increase the magnitude of the t statistic and/or the likelihood of rejecting H0 except

a smaller significance level (alpha).

sometimes we reject the null hypothesis when it is true. this is referred to as

a type 1 error

the probability of not rejecting a null hypothesis when it is actually false is called

a type 11 error

When we standardize paired data we a.convert X to a T score. b.convert both X and Y to z scores. c.divide everything by the standard deviation of X. d.subtract the mean from each value of X and Y.

convert both X and Y to z scores.

if the test scores on an art history exam were normally distributor with a mean of 76 and standard deviation of 6, we can say

about 2.5% of students scored below 64 almost equal numbers of students scored a 70 and an 82

for a normal distribution

about 2/3 of the distribution lies within one standard deviation from the mean

I am looking down on a parking lot, and can see that about 10% of the cars are red and about 15% of the cars are blue. To estimate the probability that the next car to leave the lot will be red or blue, I would

add those two percentages

i am looking down on a parking lot and can see that about 10% of the cars are red and about 15% of the cars are blue. to estimate the probability that the next car to leave the lot will be red or blue, i would

add those two percentages

If the test scores on an art history exam were normally distributed with a mean of 76 and a standard deviation of 6, we would expect

almost equal numbers of students scored a 70 and an 82

if we compute 95% confidence limits on the mean as (112.5, 118.4): we can conclude that

an interval computed in this way has a probability of .95 of bracketing the population mean

If you transformed the following distribution into a z-score distribution, what would be the z-score for 5? X 6 12 5

answer: -0.70 The standard deviation of the distribution is 3.785939. x-xbar for the value of 5 is 5-7.666667 = -2.66667 Divide this by the standard deviation (SD), you get -.70436. Rounded to the nearest 2 decimal points is -.70 x 6 12 5 x-xbar -1.66667 4.33333 -2.66667 x-xbar\SD -0.440226322 1.144585267 -0.704361586

Suppose that you had a child who took an achievement test that has a mean of 100 and standard deviation of 10 in the population. If your child's score was 105, what is the probability that a random child would score higher than your child? Please round your answer to the nearest 4 decimal places.

answer: 0.3085 z = X - mean divided by SD z = 105 - 100 / 10 = 5 / 10 = 0.50 Your child's score is above the mean and we want to know the probability of a random child scoring higher. That means we look in the smaller portion of the z-table for a z-score of 0.50 and we find .3085.

the t distribution

approaches the normal distribution as its degrees of freedom increases

If behavior problem scores are normally distributed, and we want to say something meaningful about what values are likely and what are unlikely, we would have to know:

both the mean and the standard deviation

to find the sampling distribution of the mean we would

calculate many means and plot them

knowing that data are normally distributed allows you to

calculate what range of values are unlikely to occur by chance calculate the probability of obtaining a score greater than some specified value

An outlier

can be either an extreme score or an error that snuck into the data

Given the 1 classification chi-square setup below, what would be the obtain chi-square value? For some context, pretend that this is a situation in which someone randomly picks rock, paper, and scissors in a game and he claims that he is picking rock, paper, and scissors at random. We are testing whether he is making the choices at random. rock paper scissors Total Observed 30 62 48 150

chi square =sum 11.02857143 answer: 11.03

If you wanted to test whether men and women are equally likely to be Republicans or Democrats, which statistic would you use?

chi-square

Assume that your class took an exam last week and the mean and standard deviation of the exam were 85 and 5, respectively. Your instructor told you that 30 percent of the students had a score of 90 or above. You would probably:

conclude that the scores were not normally distributed

The interquartile range:

contains the middle 50% of scores in a data set.

Spearman's correlation coefficient (rS ) applies to

data that have been converted to ranks.

____________ is an adjustment to sample size when you use sample statistics to estimate population parameters.

degree of freedom (df)

The ordinate of a normal distribution is often labeled

density.

Which two variables have the strongest relationship? Correlations SPSS output.pdf

eahtot and itn of r = .416

if a set of events contains all of the possible outcomes, it is said to be

exhaustive

we are most likely to reject a null hypothesis if the test statistic we compute is

extreme

a type II error refers to

failing to reject a null hypothesis

If you have a small correlation, you will not need a large sample size to get a power of .80

false. Small effect sizes require large sample to achieve a power of .80 or grater.

if we erroneously conclude that motorists are not more likely to honk at low status cars than high status cars (when in truth there is a difference), we

have made a type 11 error

People in the stock market refer to a measure called the "standard deviation," although it is calculated somewhat differently from the one discussed here. It is a good guess that this measure refers to:

how much the stock price is likely to fluctuate

Where is "subjective probability" most likely to be invoked?

in deciding if tomorrow will be a good day

which is true?

in null hypothesis testing, we compare our sample statistic to a theoretical distribution in order to make inferences about a population.

If your were testing the null hypothesis that women score higher on a continuous measure of empathy than men, which test statistic would you use?

independent sample t-test

Hypothesis testing is necessarily part of

inferential statistics

a confidence interval computed for the mean of a single sample

is associated with a probability about the location of a population of mean

A reliable correlation is one that a.is non-negative. b.is likely to be closely approximated in a future study. c.is significantly different from 0. d.is close to 1.00.

is likely to be closely approximated in a future study.

a normal distribution

is symmetrical

We generally like the standard deviation when we are trying to describe a sample of data because:

it allows for more intuitive interpretation with respect to the data than does the variance.

The disadvantage of using an interquartile range is that:

it discards too much of the data

which of the following is not always true of a standard normal distribution

it is skewed

which of the following is not always true of a normal distribution

it is skewed it has a mean of 0

As you increase the number of observations in a sample from 50 to 500, you are most likely to

leave the mean and standard deviation approximately unchanged

When calculating the standard deviation we divide by N-1 rather than N because the result is:

less biased

by convention, we often reject the null hypothesis if the probability of our result, given then the null hypothesis were true, is

less than .05

for a t test with one sample we

lose one degree of freedom because we estimate the mean

A researcher was interested in seeing if males or females in large lecture classes fell asleep more during in-class videos. The null hypothesis of this study is

males and females fall asleep at the same rate

a researcher was interested in seeing if males or females in large lecture classes fell asleep more during in-class videos. the null hypothesis of this study is

males and females fall asleep at the same rate

Data points at the extremes of the distribution have:

more effect on the variance than scores at the center of the distribution

If you wanted to predict grade point averages, with three independent variables (i.e. number of hours studies, self-efficacy beliefs, and math skills), which test statistic would you use? GPA is a quantitative (continuously measured) variable.

multiple regression

A linear transformation of data:

multiplies all scores by a constant and/or adds some constant to all scores

a 95% confidence interval is going to be __ a 99% confidence interval

narrower than

if the population from which we draw very large sample is "rectangular": then the sampling distribution of the mean will be roughly

normal

If the correlation between a body image measure and an eating disorders measure is .50, we can conclude that

one quarter of the variability in the eating disorders scores is associated with variability in body image.

when we are willing to reject the null hypothesis only when the outcome is bigger than expected, we are making a

one-tailed test

What correlation is used to find the association between two interval/ratio scales. a. Spearman b. Pearson c. phi d. point biserial

pearson Pearson is used for the correlation between two interval/ratio variables.

There are a few z scores that we use often that are worth remembering. The lower 2 1/2 %, and upper 2 1/2 percent of a normal distribution are cut off by z scores of:

plus and minus 1.96

If I want to find the association between a dichotomous variable and a variable measured at the interval level, I would use what correlation? a. phi b. Peason c. point biserial d. Spearman

point biserial Point biserial correlations are between a dichotomous variable and an inverval/ratio variable

A newspaper headline writer found that the more adjectives she put in the titles of her articles, the greater the number of newspapers that were sold that day. This relationship between numbers of adjectives and newspaper sales must be

positive

If the whiskers on a boxplot are much longer on the right than on the left, we would suspect that the distribution is:

positively skewed

Which of the following is NOT a method of describing data that reduces the role of outliers on the measurement of a data set's variability?

range

a type 1 error has occurred if we

reject a null hypothesis that is really true

If you were testing the null hypothesis that a group of 20 patients in the hospital had improved blood pressure when they are released from the hospital, compared to when they entered the hospital,, which test statistic would you use? Blood pressure is a quantitative, continuously measured, variable.

related sample t-test

The vertical line in the center of a box plot

represents the sample median

the sampling distribution of the mean typically

resembles a normal distribution

If the data are reasonably consistent with the null hypothesis, we are likely to

retain the null hypothesis

if the data are reasonably consistent with the null hypothesis, we are likely to

retain the null hypothesis

Which of the following is the null hypothesis when you use the correlation coefficient? a. rho = 0 b. there is a relationship between the two variables c. there is not a null hypothesis when you test the significance of r. d. The correlation will not be negative

rho=0 The null hypothesis is that the population correlation (i.e. rho) will be zero.

if behavior problem scores are roughly normally distributed in the population, then we can say that

roughly 2/3 of the sample should fall within 1 standard deviation of the mean the sample distribution should more closely resemble a normal distribution as n increases

Which correlation (i.e. between what two variables) is not significant using an alpha of 0.05?

sefamily and wrtot, with a p-value of 0.106

the difference between normal distribution and a standard normal distribution is

standard normal distributions always have a mean of 0 and a standard deviation of 1

The difference between a normal distribution and a standard normal distribution is

standard normal distributions always have a mean of 0 and a standard deviation of 1.

an example of linear transformation is

subtracting the value of the mean from each individual IQ score and dividing by the value of the standard deviation converting heights from feet to meters

the two-tailed p value that a statistical program produces refers to

the probability of getting at least that large an absolute value of t if the null hypothesis is true

if we have run a t test with 35 observations and have found a t of 3.60 which is significant at the level .05 level: we would write

t(34) = 3.60, p <.05

If you wanted to test the significance of the difference between men and women IQ scores, which statistic would you use?

t-test

sampling distributions help us test hypothesis about means by

telling us what kinds of means to expect if the null hypothesis is true

If the correlation between X and Y is significant, that tells us a.nothing about the regression equation. b.that the slope is significant. c.that X causes Y. d.that the intercept is significant.

that the slope is significant.

if we fail to reject the null hypothesis in a t test we can conclude

that we do not have enough evidence to reject the null hypothesis

the term "effect size" refers to

the actual magnitude of the mean or difference between means

Using the example from the text about the supermarket fliers, when we calculate the probability that a flier will be left either among the canned goods or in the bottom of the shopping cart, we need to invoke

the additive rule

hypothesis testing

the application of a statistical test to determine whether an observation or idea is to be refuted or supported.

the value of the test statistic that would lead us to reject the null hypothesis is called

the critical value

Which of the following is NOT a measure of variability?

the density

The tables of the standard normal distribution contain only positive values of z. This is because:

the distribution is symmetric

tables of the standard normal distribution often contain only positive values of z. this is because

the distribution is symmetric

two events are said to be independent if

the occurrence of one has no effect on the probability of the occurrence of the other

Two events are said to be independent if

the occurrence of one has no effect on the probability of the occurrence of the other.

an assumption behind the use of a one-sample t test is that

the population is normally distributed

the symbol p is commonly used to refer to

the probability of an event

a type II error concerns

the probability of not rejecting a false null hypothesis

the area that encompasses the extreme 5% of a distribution is frequently referred to as

the rejection region

the hypothesis that we are trying to support by running an experiment is often called

the research hypothesis

When we have considerable spread of the points about the regression line, the slope of that line will be ________ the slope of a similar line when there is less scatter.

the same as

a one-sample t test was used to see if a college ski team skied faster than the population of skiers at a popular ski resort. the resulting statistic was t(23) = -7.13, p < .05. what should we conclude

the sample mean of the college skiers was significantly different for the population mean

If we were to repeat an experiment a large number of times and calculate a statistic such as the mean for each experiment, the distribution of these statistics would be called

the sampling distribution

if we were to repeat an experiment a large number of times and calculate a statistic such as the mean for each experiment, the distribution of these statistics would be called

the sampling distribution

Which of the following events are most likely to be independent?

the sex of your cousin's first child and the sex of your cousin's second child

if behavior problem scores are normally distributed, and we want to say something meaningful about what values are likely and what are unlikely, we would have to know

the standard deviation the mean

when you have a single sample and want to compute an effect size measure: the most appropriate denominator is

the standard deviation of the sample

the standard deviation of a sampling distribution is known as

the standard error

the distribution that is normally distributed with a mean of 0 and a standard deviation of 1 is called

the standard normal distribution

The difference between a standard score of -1.0 and a standard score of 1.0 is

the standard score 1.0 is above the mean while -1.0 is below the mean

What would happen to the variance of distribution if we transformed that distribution by dividing all values in the distribution by 2?

the variance would be smaller than the variance of the original distribution

the difference between a z score of -1.0 and a z score of 1.0 is

the z score 1.0 is above the mean while -1.0 is below the mean

dr. harmon expected that her neurotic patients would come significantly earlier to all scheduled appointments compared to other patients, and planned to run a one-tailed test to see if their arrival times were much earlier. she found the opposite result: the neurotic patients came to appointments later than other patients. what can dr. harmon conclude from her one-tailed test

there is no compelling evidence that neurotic patients came earlier than other patients

if a population of behavior problem scores is reasonably approximated by a normal distribution, we would expect that the X axis would

too little information to determine

An assumption of the Pearson Product Moment correlation is that the relationship between two variables is linear.

true

Z-scores allow us to compare apples to oranges. In other words, even though the mean and standard deviation of scores in you math class are different than the mean and standard deviation of scores in your English class, you can still transform your math and English scores into z-scores and tell which class you are doing better in--compared to other students in your classes.

true Because z-distributions always have the same mean and standard deviation, you can compare any z-score with any other z-score.

When you transform any distribution into a z-score distribution, the mean of the new distribution will always be zero and the standard deviation of the new distribution will always be 1.0.

true bc z-score distributions always have a mean of zero and standard deviation of 1.0.

when we are willing to reject the null hypothesis when the outcome is either bigger than expected or smaller than expected, we are making a

two-tailed test

Sometimes we reject the null hypothesis when it is true. This is technically referred to as

type I error

which of the following pairings is correct

type I; Type II:: a;B

If we look at the correlation between college admissions test scores and subsequent performance in college for all admitted applicants, we are likely to

underestimate the degree of correlation between test score and potential performance

The population variance is

usually an unknown that we try to estimate

The population variance is _____?

usually an unknown that we try to estimate

The population variance is:

usually an unknown that we try to estimate

In plotting the relationship between the incidence of breast cancer and the level of vitamin D in the body, we would most likely plot

vitamin D on the X axis and incidence of breast cancer on the Y axis

we are interested in what the text calls "probable limits" because

we want to have a good idea what kinds of values to expect we want to know whether a piece of data is unusual

if the population from which we sample is positively skewed: the sampling distribution of the mean

will approach normal for large sample sizes

if the population from which we sample is normal: the sampling distribution of the mean

will be normal