(ACTUAL) - Test #3 - Stats

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

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

100

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

degree of freedom (df)

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.

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)

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

The population variance is _____?

usually an unknown that we try to estimate

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

1 1/2 standard deviations below the mean.

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

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.

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

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

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

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

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

12

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.

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

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

2.08

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 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 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

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.

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 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.

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.

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

The variance is 16 and the standard deviation is 4.00.

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.

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

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

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.

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

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

less biased

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

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.