STATS 212 - CHAPTER 7, 8, and 9 LEARNING CHECKS

9. on average, what value is expected for the t stat when the null hypothesis is true? 0 1 1.96 1 > 1.96

0

7. if random samples, each with n = 9 scores, are selected from a normal population with μ = 80 and σ = 18, and the mean is calculated for each sample, then how much distance is expected on average between and μ 2 points 6 points 18 points cannot be determined w/o additional inforomation

6 points

7. T/F: a sample mean with z = 3.00 is a fairly typical, representative sample

FALSE

7. T/F: the mean of the sample is always equal to the population mean

FALSE

7. T/F: the shape of the distribution of sample means is always normal

FALSE

9. T/F sample size has a great influence on measures of effect size

FALSE

7. a random sample is selected from a population with μ = 80 and σ = 20. how large must the sample be to ensure a standard error of 2 points or less? n ≥ 10 n ≥ 25 n ≥ 100 it is impossible to obtain a standard error of less than 2 for any sized sample

n ≥ 200

8. a researcher uses a hypothesis test to evaluate H0: μ = 80. which combination of factors is most likely to result sin rejecting the null hypothesis? σ = 5 and n = 25 σ = 5 and n = 50 σ = 10 and n = 25 σ = 10 and n = 50

σ = 5 and n = 50

7. a random sample of n = 4 scores is obtained from a normal population with μ = 40 and σ = 6. what is the probability of obtaining a mean greater than M = 46 for this sample? 0.3085 0.1587 0.0668 0.0228

0.0228

7. a random sample of n = 4 scores is obtained from a normal population with μ = 20 and σ = 4. what is the probability of obtaining a mean greater than M = 22 for this sample? 0.50 1.00 0.1587 0.3085

0.1587

7. a sample of n = 4 scores has a standard error of 12. what is the standard deviation of the population from which the sample was obtained? 48 24 6 3

24

7. A population has μ = 60 with σ = 5; the Distribution of sample means for samples of size n = 4 selected from this population would have an expected value of _____. 5 60 30 15

60

7. if all the possible random samples, each with n = 9 scores, are selected from a normal population with μ = 18, and the mean is calculated for each sample, then what is the average value for all of the sample means? 9 80 9(80) = 729 cannot be determined without additional information

80

7. if random samples, each with n = 4 scores, are selected from a normal population with μ = 80 and σ = 10, then what is the expected value of the mean for the distribution of sample means? 2.5 5 40 80

80

8. T/F: a decision to retain the null hypothesis means that you proved that the treatment has no effect

FALSE

8. T/F: a type II error is like convicting a guilty person in a jury trial

FALSE

8. T/F: increasing the sample size will also increase the effect size

FALSE

8. T/F: lowering the alpha level from 0.05 to 0.01 will increase the power of a statistical test

FALSE

8. T/F: when the z-score is quite extreme, it shows that the null hypothesis is true

FALSE

9. T/F by chance, two samples selected from the same population have the same size (n = 36) and the same mean ( M = 83). that means they will also have the same t statistic

FALSE

9. T/F compared to a z-score, a hypothesis test with a t statistic requires less information about the population

FALSE

9. T/F when the value of the t statistic is near 0, the null hypothesis should be rejected

FALSE

7. for a normal population with μ = 80 and σ = 20, which of the following samples is least likely to be obtained? M = 88 for a sample of n = 4 M = 84 for a sample of n = 4 M = 88 for a sample of n = 25 M = 84 for a sample of n = 25

M = 88 for a sample of n = 25

7. for a sample selected from a normal population with μ = 100 and σ = 15, which of the following would be the most extreme and unrepresentative? M = 90 for a sample of n = 9 scores M = 90 for a sample of n = 25 scores M = 95 for a sample of n = 9 scores M = 95 for a sample of n = 25 scores

M = 90 for a sample of n = 25 scores

7. T/F: as sample size increases, of the value of the standard error decreases

TRUE

8. T/F: a type I error is like convicting an innocent person in a jury trial

TRUE

8. T/F: an effect that exists is less likely to be detected if σ is large

TRUE

8. T/F: an effect that exists is more likely to be detected if n is large

TRUE

8. T/F: cohen's d is used because alone, a hypothesis test does not measure the size of the treatment effect

TRUE

8. T/F: if the alpha level is decreased, the size of the critical region decreases

TRUE

8. T/F: larger differences between the sample and population mean increase effect size

TRUE

8. T/F: the critical region defines unlikely values if the null hypothesis is true

TRUE

7. a sample is obtained from a population with μ = 100 and σ = 20. which of the following samples would produce the z-score closest to zero? a sample of n = 25 scores with M = 102 a sample of n = 100 scores with M = 102 a sample of n = 25 scores with M = 104 a sample of n = 100 scores with M = 104

a sample of n = 25 scores with M = 102

8. how is the power of a hypothesis test related to sample size and the alpha level? a. a larger sample and a larger alpha level will both increase power b. a larger sample and a larger alpha level will both decrease power c. a larger sample will increase power but a larger alpha will decrease power d. a larger sample will decrease power but a larger alpha will increase power

a. a larger sample and a larger alpha level will both increase with power

8. a sample of n = 4 individuals is selected from a population with μ = 80 and σ = 5, and a treatment is administered to the sample. if the treatment really does have an effect, then what would be the effect of increasing the sample size to n = 25? a. increase the chances that the sample will produce an extreme z-score and increase the likelihood that you'll conclude a treatment effect exists b. increase the chances that the sample will produce an extreme z-score and increase the likelihood that you'll conclude that a treatment effect does not exist c. increase the chances that the sample will produce a z-score near zero and increase the likelihood that you'll conclude a treatment effect exists d. increase the chances that the sample will produce a z-score near zero and increase the likelihood that you'll conclude a treatment effect does not exist

a. increase the chances that the sample will produce an extreme z-score and increase the likelihood that you will conclude that a treatment effect exists

8. how does the sample size influence the likelihood of rejecting the null hypothesis and the power of the hypothesis test? a. increasing sample size increases both the likelihood of rejecting null and the power of the test b. increasing sample size decreases both the likelihood of rejecting null and the power of the test c. increasing sample size increases the likelihood of rejecting null but the power of the test is unchanged d. increasing sample size decreases the likelihood of rejecting null but the power of the test is unchanged

a. increasing sample size decreases both the likelihood of rejecting null and the power of the test

8. what is the consequence of increasing the alpha level (for example, from 0.01 to 0.05)? a. it will increase the likelihood of rejecting null and increase the risk of a type I error b. it will decrease the likelihood of rejecting null and increase the risk of a type I error c. it will increase the likelihood of rejecting null and decrease the risk of a type I error d. it will decrease the likelihood of rejecting null and decrease the risk of a type I error

a. it will increase the likelihood of rejecting null and increase the risk of a type I error

8. which of the following accurately describes the critical region for a hypothesis test? a. outcomes that have a very low probability if the null hypothesis is true b. outcomes that have a high probability if the null hypothesis is true c. outcomes that have a very low probability whether or not the null hypothesis is true d. outcomes that have a high probability whether or not the null hypothesis is true

a. outcomes that have a very low probability if the null hypothesis is true

8. if the power of a hypothesis test is found to be p = 0.80, then what is the probability of a type II error for the same test? a. p = 0.20 b. p = 0.80 c. the probability of a type II error is not related to power d. it's impossible to determine without knowing the alpha level for the test

a. p = 0.20

9. a sample is selected from a population and a treatment is administered to the sample. for a hypothesis test with a t statistic, if there is a 5-point difference between the sample mean and the original population mean, which set of sample characteristics is most likely to lead to a decision that there is a significant treatment effect? a. small variance for a large sample b. small variance for a small sample c. large variance for a large sample d. large variance for a small sample

a. small variance for a large sample

8. a research report includes the statement, "z = 2.18, p < 0.05)." what happened in the hypothesis test? a. the obtained sample mean was very unlikely if the null hypothesis is true, so null was rejected b. the obtained sample mean was very likely if the null hypothesis is true, so null was rejected c. the obtained sample mean was very unlikely if the null hypothesis is true, and the test failed to reject null d. the obtained sample mean was very likely if the null hypothesis is true, and the test failed to reject null

a. the obtained sample mean was very unlikely if the null hypothesis is true, so null was rejected

8. a sample of n = 25 individuals is selected from a population with μ = 80 and a treatment is administered to the sample. which of the following is the most likely outcome if the treatment has a large effect? a. the sample mean should be very different from 80 and should lead you to reject the null hypothesis b. the sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis c. the sample mean should be close to 80 and should lead you to reject the null hypothesis d. the sample mean should be close to 80 and should lead you to fail to reject the null hypothesis

a. the sample mean should be very different from 80 and should lead you to reject the null hypothesis

9. a hypothesis test produces a t statistic of t = 2.30. if the researcher is using a two-tailed test with a = 0.05, how large does the sample have to be in order to reject the null hypothesis a. at least n = 8 b. at least n = 9 c. at least n = 10 d. at least n = 11

at least n = 10

9. a sample of n = 25 is selected from a population with μ = 40, and a treatment is administered to each individual in the sample. after treatment, the sample mean is M = 44 with a sample variance of s^2 = 100. based on this information, what's the size of the treatment effect as measured by cohen's d? d = 0.04 d = 0.40 d = 1.00 d = 2.00

b. 0.40

9. when n is small (less than 30), the t distribution _____ a. is almost identical in shape to the normal z distribution b. is flatter and more spread out than the normal z distribution c. is taller and narrower than the normal z distribution d. cannot be specified, making hypothesis tests impossible

b. is flatter and more spread out than the normal z distribution

8. which of the following defines a type I error? a. rejecting a false null hypothesis b. rejecting a true null hypothesis c. failing to reject a false null hypothesis d. failing to reject a true null hypothesis

b. rejecting a true null hypothesis

9. a researcher uses a sample of n = 25 individuals to evaluate the effect of a treatment. the hypothesis test uses a = 0.05 and produces a significant result with t = 2.15. how would this result be reported in literature? a. r(25) = 2.15, p < 0.05 b. r(24) = 2.15, p < 0.05 c. t(25) = 2.15, p > 0.05 d. r(24) = 2.15, p > 0.05

b. t(24) = 2.15, p < 0.05

9. the results of a hypothesis test are reported as follows: t(21) = 2.38, p < 0.05. what was the statistical decision and how big was the sample? a. the null hypothesis was rejected using a sample of n = 21 b. the null hypothesis was rejected using a sample of n = 22 c. the null hypothesis was not rejected using a sample of n = 21 d. the null hypothesis was not rejected using a sample of n = 22

b. the null hypothesis was rejected using a sample of n = 22

8. under what circumstances can a very small treatment effect be statistically significant? a. with a large sample and a large SD b. with a large sample and a small SD c. with a small sample and a large SD d. with a small sample and a small SD

b. with a large sample and a small SD

8. a researcher is predicting that a treatment will decrease scores. if this treatment is evaluated using a directional hypothesis test, then the critical region for the test _____. a. would be entirely in the right-hand tail of the distribution b. would be entirely in the left-hand tail of the distribution c. would be divided equally between the two tails of the distribution d. cannot answer without knowing the value of the alpha level

b. would be entirely in the left-hand tail of the distribution

8. a sample of n = 9 scores is selected from a population with a mean of μ = 80 and σ = 12, and a treatment is administered to the sample. after the treatment, the researcher measures effect size with Cohen's d and obtains d = 0.25. what was the sample mean? a. M = 81 b. M = 82 c. M = 83 d. M = 84

c. M = 83

8. if other factors are held constant, then how does sample size affect the likelihood of rejecting the null hypothesis and the value for cohen's d? a. a larger sample increases the likelihood of rejecting the null and increases the value of cohen's d b. a larger sample increases the likelihood of rejecting the null but decreases the value of cohen's d c. a larger sample increases the likelihood of rejecting the null but has no effect on the value of cohen's d d. a larger sample decreases the likelihood of rejecting the null but has no effect on the value of cohen's d

c. a larger sample increases the likelihood of rejecting the null hypothesis but has no effect on the value of cohen's d

8. what does a type II error mean? a. a researcher has falsely concluded that a treatment has an effect b. a researcher has correctly concluded that a treatment has no effect c. a researcher has falsely concluded that a treatment has no effect d. a researcher has correctly concluded that a treatment has an effect

c. a researcher has falsely concluded that a treatment has no effect

8. in general terms, what is a hypothesis test? a. a descriptive technique that allows researchers to describe a sample b. a descriptive technique that allows researchers to describe a population c. an inferential technique that uses the data from a sample to draw inferences about a population d. an inferential technique that uses information about a population to make predictions about a sample

c. an inferential technique that uses information about a population to make predictions about a sample

8. the power of a statistical test is the probability of _______ a. rejecting a true null hypothesis b. supporting a true null hypothesis c. rejecting a false null hypothesis d. supporting a false null hypothesis

c. rejecting a false null hypothesis

9. in what circumstances is the t statistic used instead on a z-score for a hypothesis test? a. the t stat is used when the sample size n = 30 or larger b. the t stat is used when the population mean is unknown c. the t stat is used when the population variance (or SD) is unknown d. the t stat is used if you are not sure that the population distribution is normal

c. the t stat is used when the population variance (or SD) is unknown

9. a sample of n = 4 scores is selected from a population with an unknown mean. the sample has a M - 40 and a variance of s^2 = 16. which of the following is the correct 90% confidence interval for μ? a. μ = 40 +- 2.353(4) b. μ = 40 +- 1.638(4) c. μ = 40 +- 2.353(2) d. μ = 40 +- 1.638(2)

c. μ = 40 +- 2.353(2)

9. a sample is selected from a population with a mean of μ = 75, and a treatment is administered to the individuals in the sample. the researcher intends to use a t statistic to evaluate the effect of the treatment. if the sample mean is M = 79, then which of the following outcomes would produce the largest value for cohen's d? a. n = 4 and s^2 = 30 b. n = 16 and s^2 = 30 c. n -25 and s^2 = 30 d. all three samples would produce the same value for cohen's d

d. all three samples would produce the same value for cohen's d

8. what assumptions is needed before you can use the unit normal table to find critical values for a z-score hypothesis test? a. the population of scores before treatment is normal b. the scores are obtained by random sampling c. the scores in the sample are independent observations d. the distribution of sample means is normal

d. the distribution of sample means is normal

9. a sample of n = 4 scores has SS = 48. what is the estimated standard error for the sample 48 16 4 2

d. the t stat is used if you are not sure that the population distribution is normal

7. all of the possible random samples of size n = 2 are selected from a population with μ = 40 and σ = 10 and the mean is computed for each sample. then all the possible samples of size n = 25 are selected from the same population and the mean is computed for each sample. how will the distribution of sample means for n = 2 compare with the distribution for n = 25? a. the two distributions will have the same mean and variance b. the mean and the variance for n = 25 will both be larger than the mean and variance for n = 2 c. the mean and variance for n = 25 will both be smaller than the mean and variance for n = 2 d. the variance for n = 25 will be smaller than the variance for n = 2 but the two distributions will have the same mean

d. the variance for n = 25 will be smaller than the variance for n = 2 but the two distributions will have the same mean

7. which of the following would cause the standard error of M to get smaller? a. increasing both the sample size and standard deviation b. decreasing both the sample size and standard deviation c. increasing the sample size and decreasing the standard deviation d. decreasing the sample size and increasing the standard deviation

increasing the sample size and decreasing the standard deviation

7. a sample obtained form a population with σ = 10 has a standard error of 2 points. how many sores are in the sample? n = 5 n = 10 n = 20 n = 25

n = 25

9. a sample of n = 9 scores is selected from a population with a mean of μ = 70, and a treatment is administered to the sample. after treatment, the sample has M = 74 and SS = 288. if a hypothesis test with a t statistic is used to evaluate the treatment effect, then what value will be obtained for the t statistic? t = 1 t = 1.50 t = 2 t = 4

t = 2

8. a sports coach is investigating the impact of a new training method. in words, what would the null hypothesis say? a. the new training program produces different results from the existing one b. the new training program produces results similar to the existing one c. the new training program produces better results than the existing one d. there is no way to predict the results of the new training program

the new training program produces results similar to the existing one

7. if all the possible random samples of size n = 25 are selected from a population with μ = 80 and σ = 10 and the mean is computed for each sample, then what shape is expected for the distribution of sample means? a. the same means tend to form a normal-shaped distribution b. the distribution of sample means will have the same shape as the sample distribution c. the sample will be distributed evenly across the scale, forming a rectangular-shaped distribution d. there are thousands of possible samples and it is impossible to predict the shape of the distribution

the sample means tend to form a normal-shaped distribution

7. a sample of n = 16 scores is obtained from a population with μ = 70 and σ = 20. if the sample mean is M = 75, then what is the z-score corresponding to the sample mean? z = 0.25 z = 0.50 z = 1.00 z = 2.00

z = 1.00

7. A random sample of n = 16 scores is obtained from a population with μ = 50 and σ = 16. If the sample mean is M = 58, the z-score corresponding to the sample mean is ____? z=1.00 z=2.00 z=4.00 cannot determine

z = 2.00

8. a sample is selected form a population with a mean of μ = 60 and a treatment is administered to the individuals in the sample. if a hypothesis test is used to evaluate the treatment effect, then what's the correct statement of the null hypothesis? μ = 60 μ ≠ 60 M = 60 M ≠ 60

μ = 60

9. a sample is selected from a population with a mean of μ = 30 and a treatment is administered to the sample. if the treatment is expected to increase scores and a t statistic is used for a one-tailed hypothesis test, then which of the following is the correct null hypothesis? μ ≤ 30 μ < 30 μ ≥ 30 μ > 30

μ ≤ 30