Statistics test 3

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 115, what is the probability that a random child would score higher than your child? Please round your answer to the nearest 4 decimal places.

0.0668

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 82? 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.

0.09

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 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 a standard deviation of 10. The clinic decides to find the highest 5 % of scores. What is the score that marks the 95th percentile? Round your answer to the nearest 2 decimal places.

106.45

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. rockpaperscissors TotalObserved306248 140

11.028

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.

11.028 is value of the obtain chi-square, which is larger than the c.v., meaning we can reject the null hypothesis.

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

12

If you had a standard deviation of 12, what would be the variance?

144

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

degrees of freedom

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.

fail to reject the null hypothesis

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

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

less biased

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 hypothesis

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

Calculate the standard deviation of the following set of data X: 22 25 18

3.512

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

-0.70

What is the obtained chi-square of the following 2 x 2 contingency table? SuccessRelapseTotal Drug35.00016.00051.000 Placebo12.0008.00020.000

0.478

Based on the previous question about a 2 x 2 chi square analysis (see table below), what would you conclude about the null hypothesis? In your answer, explain how you made your decision. It is not enough to simply say you reject the null hypothesis or fail to reject the null hypothesis. YesNoDrug3516Placebo128

0.48 is the vakue for the obtain chi square, which is lower than the critical value. Therefore, it is necessary to reject the null hypothesis.

In a normally distributed distribution with a mean of 70 and a standard deviation of 5, what is the probability that a randomly selected score will fall between 67.5 and 75? 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 3 decimal places. Your answer should be in the following format ... 0.254, for example.

0.53

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

In a normally distributed distribution with a mean of 100 and a standard deviation of 10, what is the probability that a randomly selected score will fall between 95 and 115? 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. Your answer should be in the following form... 0.46, for example.

0.62

In a normally distributed distribution with a mean of 100 and a standard deviation of 10, what is the probability that a randomly selected score will fall between 90 and 110? 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. Your answer should be in the following form... 0.46, for example.

0.68

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.

2.00

Calculate the variance of the following set of data. X: 20 10 12

28

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

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?

76

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

If I fail to 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 not a difference or relationship in the study.

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

The mean 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

A z score of -1.00 represents an observation that is:

one standard deviation below the mean

here 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

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

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

The population variance is _____?

usually an unknown that we try to estimate