Ch 5 Q's, Ch 6 Questions, test #3 - Online practice work, test #3 - Stats & Methods

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

Try to make your results agree with other similar studies

alternative hypothesis

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

Hypothesis

an observation or idea that can be tested

If you transformed the following distribution into a z-score distribution, what would be the z-score for 5? X 6 12 5 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 x bar -1.66667 x-xbar -0.440226322 x 12 x bar 4.33333 x-xbar 1.144585267 x 5 x bar -2.66667 x-xbar -0.704361586 xx-xbar(x-xbar)sqz score 6-1.666672.777778 -0.44023 n =3 124.33333318.77778 1.144586 5-2.666677.111111 -0.70436 BlankBlank Blank sum =23 28.66667 mean =7.666667Var =14.33333 SD =3.785939

answer - 0.70

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

Percentiles

indicates what percentage of the data falls below a certain value Percentile of X= number of data points less than X / total number of data points

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

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

standard deviation

measures the average distance data values are from the mean. When the values in a data set are tightly bunched together, the standard deviation will be small.When the values in a data set are spread apart, the standard deviation will be relatively large. variance=σ^2

Data points at the extremes of the distribution have:

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

A linear transformation of data:

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

type I error

occurs when you incorrectly reject the null hypothesis

z-score allows comparison of the variation in different populations / samples

population: z_x= x−μ​ / σ sample: zx​=x−xbar / s​

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

Suppose your study uses an alpha of .01, your t-critical value is 1.65 and you obtain a t-statistic of -1.70. What would you conclude?

reject the null hypothesis

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

(μ ± 1.96σ)

What would be the standard deviation of the following distribution, if you divided every value by 5? x 2 5 3 4

0.258199

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%

Calculate the variance of the following distribution. Please round your answer to the nearest 2 decimal places. x 16 14 22 25

26.25

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

What would be the variance of the following distribution, if you multiplied every value by 5? x 2 5 3 4

41.67

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.

Calculate the standard deviation of the following set of data X 33 19 18

8.39

Calculate the standard deviation of the following distribution. Please round your answer to the nearest 2 decimal places. x 6 15 21 26

8.60

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

determining correlation

For each of the following scatter plots determine whether the bi variate data is positively correlated, negatively correlated, or has no correlation

which are false?

In null hypothesis testing, we are trying to determine whether there is a relationship or difference in our sample c. Null hypothesis testing is primarily interested in making a probabilistic statement about clinical significance. d. We always use an alpha of .05 in null hypothesis testing

Which of the following statements is true?

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

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 I reject the null hypothesis, what am I concluding?

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

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.

alpha

The probability of falsely rejecting the null hypothesis

Connor was a difficult child when he was young. The Behavior Problem Index (BPI) is a measure of behavior problems in youth. The population mean is 100 with a standard deviation of 15. Connor's was sent to a psychologist who administered the BPI and Connor's BPI score was 130. True or False, Connor's z-score on the BPI was 2.00 which means that his score was 2 standard deviations above the mean.

true - z = x - xbar divided by SD. = 130 - 100 divided by 15 = 30 / 15 = 2.00

The population variance is

usually an unknown that we try to estimate

The population variance is:

usually an unknown that we try to estimate

statistical significance

when the difference you observe between two samples is large enough that is is not simply due to chancery

reject the null hypothesis

when you have enough statistical strength to show a difference or an association

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

1

clinical significance

A statistically significant result that is clinically useful

If you transformed the following distribution into a z-score distribution, what would be the z-score for 6? Please round your answer to the nearest 2 decimal places. x 6 15 21 26

-1.278724026

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.

What would be the variance of the following distribution, if you divided every value by 5? x 2 5 3 4

.07

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

In a normally distributed distribution with a mean of 50 and standard deviation of 10, what is the probability that a randomly selected score will fall between 30 and 40? Your answer should be expressed as a probability(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.

0.1359. 30 is 2 SDs below the mean and 40 is 1 SD below the mean. If you use the mean to z for 2 SDs, you will have more area under the curve than the question asks for. You will need to subtract from that the area from the mean to 1 SD below the mean. 2 SD = .4772 minus 1 SD (.3413) = .1359

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 between 86 and 92? Your answer should be expressed as a probability(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.

0.1498.

If you transformed the following distribution into a z-score distribution, what would be the z-score for 19? Please round your answer to the nearest 2 decimal places. x 5 12 19 22

0.59258

In a normally distributed distribution with a mean of 70 and standard deviation of 8, what is the probability that a randomly selected score will fall between 54 and 78? Your answer should be expressed as a probability (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.

0.8185. 54 is 2 SDs below the mean and 78 is 1 SD above the mean. So, you add the mean to z for 2 SDs and the mean to z of 1 SD. = .4772 + .3413 = .8185

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 probability (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. The answer is the larger proportion of a z score of 1 in the z-table because 92 is 1 SD above the mean.

If you transformed a distribution into a z-score distribution, what would be the standard deviation of the newly created distribution?

1.0

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 subtracting 5 to each number in the distribution? X 2 4 7 8 10

1.2. The mean of the original distribution was 6.2. If we subtracted 5 from each score, the mean of the new distribution would be 1.2 because subtracting a constant from every score in the distribution reduces the mean by the amount of the constant.

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

(N-1) If you had a population that consisted of the numbers 1, 2, 3 and 4, what would be the average variance of all possible samples of sample sizes 3 when you use n-1 in the denominator of the sample variance formula? Round your answer to the nearest 2 decimal places.

1.25. The long run average of the variances taken from repeated samples from a population will equal the population variance. So, the answer would be the variance of the population which uses n in the denominator of the population variance formula. This works out to be 5 / 4 = 1.25.

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

11.2. The new distribution would be as follows with a mean of 11.2 When you add a constant, the mean increases by the constant (i.e. 6.2 + 5.0 = 11.2).

Calculate the variance of the following set of data. Please round your answer to the nearest 2 decimal places. X 20 16 12

16

Calculate the variance of the following distribution. Please round your answer to the nearest 2 decimal places. x 16 14 22

17.33

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

31. The mean of the original distribution was 6.2 and the mean of the new distribution would be 31.00 if we multiplied each score by 5. This is because the mean of a distribution is increased by a multiple of the constant when we multiple each score in a distribution by a constant.

Please calculate the standard deviation of the following set of data. X 22 12 15

5.12

What would be the standard deviation of the following distribution, if you multiplied every value by 5? x 2 5 3 4

6.45

Calculate the standard deviation of the following distribution. Please round your answer to the nearest 2 decimal places. x 11 14 22 25

6.58

The following table shows data on sentencing for white and non white (mostly Black and Hispanic) defendants in North Carolina when the victim was White. Please calculate the chi square value that can be used to evaluate whether the verdict (i.e. death sentence versus no death sentence) is independent of the defendant's race (i.e. Nonwhite verses White). Round your answer to the nearest 2 decimal points. Death Sentence: Defendant's Race Yes No Nonwhite 33 251 White 33 508

7.70-7.72. The best answer is 7.71, but I will accept 7.70 and 7.72 as well. RaceYesNoTotal O-E(O-E) squared(O-E)squared/Expected Nonwhite33.000251.000284.000 row 1 col 1 --->10.280105.6784.651expected22.720261.280 row 1 col 2 --->-10.280105.6780.404 White33.000508.000541.000 row 2 col 1 --->-10.280105.6782.442expected43.280497.720 row 2 col 2 --->10.280105.6780.212 Total66.000759.000825.000

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

fail to reject the null hypothesis

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

chi-squared formula - to estimate a population variance

X^2=(n−1)*s^2​ / σ n: sample size s: sample standard deviation σ: population standard deviation (n−1): is also called "degrees of freedom"• Chi-Square table gives critical value area to the right

You would obtain a negative value for the variance if:

You would never obtain a negative variance

The normal distribution is

a distribution with a known shape and other properties

z-score

a measure of how many standard deviations a data item xx is from the mean.

Outliers are either:

a) above Q3​+1.5(IQR) or b) below Q1​−1.5(IQR) (a data point which lies an abnormal distance from all other data points.)

which of the following are steps in hypothesis testing?

a. Decide whether to reject the null hypothesis b. Compare the distribution of the statistic to the distribution of the statistic. c. Determine what statistical test to use d. Determine the alpha level e. State the null and alternative hypotheses

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

An outlier

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

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.

The ordinate of a normal distribution is often labeled

density.

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? 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.

fail to reject the null hypo

true or false: A z-score of 2 means that the score is 2 standard deviations below the mean.

false - correct answer would be above the mean not below.

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

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

InterQuartile Range (IQR)

represents the middle 50% of the data IQR= =Q3​−Q1​

The vertical line in the center of a box plot

represents the sample median

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.

null hypothesis

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

hypothesis testing

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

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

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

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

true

true or false: A z-score of 2 means that the score is 2 standard deviations above the mean. It is not 2 standard deviations below the mean.

true

true or false: The null hypothesis cannot be proven, it can only be disproven.

true

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

true