Homework 6
The population of IQ scores forms a normal distribution with a mean of μ = 100 and a σ = 15. For a random sample of n = 36 people, the probability of obtaining a sample mean greater than M = 105 is ____. (Make sure that you take your answer to four decimal places.)
0.0228
For a population with μ = 80 and σ = 12, the z-score corresponding to a sample with a mean of M = 84 and a sample size of n = 36 is ____. (Make sure that you take your answer to two decimal places.)
2.0000
As sample size increases, the standard error of M Increases Stays constant Decreases
Decreases
The critical boundaries for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = -1.90, then what is the correct statisical decision? Fail to reject H1 Fail to reject H0 Reject H1 Reject H0
Fail to reject H0
If \alpha=.05α=.05 (one-tailed test, upper tail critical), what is the decision for zobt = -3.30? Reject the null hypothesis Fail to reject the null hypothesis (retain the null hypothesis)
Fail to reject the null hypothesis (retain the null hypothesis)
The distribution of sample means (for a specific sample size) consists of the sample means for all the possible samples (for the specific sample size) all the scores contained in the sample all the scores contained in the population the mean computed for the specific sample of scores
the sample means for all the possible samples (for the specific sample size)
In general, the null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment). True False
true
A researcher reports the following result for a one-independent sample z-test at a .05 level of significance: z = 1.88, p = .06 (d =.25). Is this result significant? yes, the decision is to reject the null. no, the decision is to retain the null. yes, because the effect size is large. no, because the effect size is small.
yes, the decision is to reject the null.
A population is known to have a mean of μ = 45 . If a researcher predicts that the experimental treatment will produce a decrease in the scores, then the null hypothesis for a one-tailed test would state _____. μ > 45 μ < 45 M > 45 M < 45
μ < 45
In a hypothesis test, the critical region consist of - sample values that are very unlikely to occur if the null hypothesis is true - sample values that are very likely to occur if the null hypothesis is true - sample values that are very unlikely to occur if the null hypothesis is false - sample values that prove that the null hypothesis is true
sample values that are very unlikely to occur if the null hypothesis is true
The population of IQ scores forms a normal distribution with a mean of μ = 100 and a σ = 15. For a random sample of n = 9 people, the probability of obtaining a sample mean greater than M = 105 is ____. (Make sure that you take your answer to four decimal places.)
0.1587
A sample of n = 25 scores has a mean of M = 84. If this sample was obtained from a population with μ = 80 and σ = 40, the z-score for this sample would be ____. (Make sure that you take your answer to two decimal places.)
0.5000
A population of scores forms a normal distribution with a mean of μ = 80 and a σ = 10. For a sample of n = 4, the proportion of scores that will have values between 75 and 85 is ____. (Make sure that you take your answer to four decimal places.)
0.6826
A population of scores forms a normal distribution with a mean of μ = 80 and a σ = 10. For a sample of n = 16, the proportion of scores that will have values between 75 and 85 is ____. (Make sure that you take your answer to four decimal places.)
0.9544
If a hypothesis test results in rejecting the null hypothesis, then the researcher must conclude that the treatment "does not have a significant effect." True False
False
The level of significance for a hypothesis test is: the probability to incorrectly rejecting the null hypothesis the probability of committing a Type I error the alpha level all of the above
all of the above
The standard deviation of the distribution of sample means is called Sample mean Central limit mean Expected value of M Standard error of M
Standard error of M
If the sample size is increased from n = 20 to n = 50, what happens to the size of the critical region. It increases It decreases The sample size has no influence on the size of the critical region.
The sample size has no influence on the size of the critical region.
What will increase the power of a hypothesis test? change a from .05 to .01 change the sample size from 25 to 100 change from a one-tailed test to a two-tailed test none of the other will increase power
change the sample size from 25 to 100
What are the critical values for a one-independent sample nondirectional (two-tailed) z-test at a .05 level of significance? ±1.26 ±1.96 ±2.12 ±2.92
±1.96
For a population with μ = 80 and σ = 12, the z-score corresponding to a sample with a mean of M = 76 and a sample size of n = 9 is ____. (Make sure that you take your answer to two decimal places.)
-1.0000
If the obtained sample data are in the critical region, then the correct decision is to reject the null hypothesis. True False
True
The alpha level determines the risk of a Type I error. True False
True
A population of scores forms a normal distribution with a mean of μ = 80 and a σ = 10. For a sample of n = 16, the proportion of scores that will have values between 75 and 85 is ____. (Make sure that you take your answer to four decimal places.)
9544.
Samples of size n = 4 are selected from a population with μ = 80 with σ = 8. What is the standard error for the distribution of sample means? 2 8 80 4
4
For a population with μ = 80 and σ = 20, the distribution of sample means based on n = 16 will have an expected value of ____ and a standard error of ____. 80, 5 20, 20 5, 80 80, 1.25
80, 5
If α=.01 (two-tailed test), what is the decision for zobt = 2.10? Reject the null hypothesis Fail to reject the null hypothesis (retain the null hypothesis)
Fail to reject the null hypothesis (retain the null hypothesis)
If the alpha level is increased from α=.01 to α=.05, what happens to the size of the critical region? It increases It decreases The alpha level has no influence on the size of the critical region
It increases
If α=.05 (one-tailed test, upper tail critical), what is the decision for zobt= 1.70? Reject the null hypothesis Fail to reject the null hypothesis (retain the null hypothesis)
Reject the null hypothesis
A hypothesis test is being used to evaluate a treatment effect with \alpha=.05α=.05 (two-tailed). If the sample data produce a z-score of z = -2.24, then what is the correct decision? Reject the null hypothesis and conclude that the treatment has no effect. Reject the null hypothesis and conclude that the treatment has an effect. Fail to reject the null hypothesis and conclude that the treatment has no effect. Fail to reject the null hypothesis and conclude that the treatment has an effect.
Reject the null hypothesis and conclude that the treatment has an effect.
f the sample is located in the critical region with α=.01, then the sample would definitely be in the critical region if alpha is changed to α=.05. True False
True
A researcher incorrectly decides to retain a null hypothesis that is actually false. The researcher committed a: Type I error Type II error Type III error All of the above
Type II error
A researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 2.77. Assuming that the researcher is using a two-tailed test, - the researcher rejects the null hypothesis with a=.05 but not with a=.01. - the researcher should reject the null hypothesis with either a=.05 or a=.01. - the researcher should fail to reject H0 with either a=.05 or a=.01. - cannot answer without additional information.
the researcher should reject the null hypothesis with either a=.05 or a=.01.
