Statistics Quiz 3- Ch.7: Probability and Samples
If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that μ = 80?
M = 85 and large sample variance
Under what circumstances will the distribution of sample means be normal?
only if the population distribution is normal
If a hypothesis test produces a z-score in the critical region, what decision should be made?
reject the null hypothesis
On average, what value is expected for the t statistic when the null hypothesis is true?
0
A random sample of n = 4 scores is obtained from a normal population with µ = 30 and σ = 8. What is the probability that the sample mean will be smaller than M = 22?
0.0228
If random samples, each with n = 4 scores, are selected from a normal population with µ = 80 and σ = 36, what is the standard error for the distribution of sample means?
18
A sample of n = 100 scores is selected from a population with μ = 80 with σ = 20. On average, how much error is expected between the sample mean and the population mean?
2 points
A sample of n = 4 scores has SS = 60. What is the variance for this sample?
20
A researcher is using a two-tailed hypothesis test with α = .05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?
22
A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8, and the sample mean is M = 43. What is the standard error for the sample mean?
4
A sample of n = 16 scores is selected from a population with μ = 80 with σ = 20. On average, how much error would be expected between the sample mean and the population mean?
5 points
Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the standard error for the distribution of sample means?
6
What is measured by the denominator of the z-score test statistic? a. A likely distance between M and µ that would be expected if H0 was true b. The actual distance between M and µ c. The position of the sample mean relative to the critical region d. Whether or not there is a significant difference between M and µ
A likely distance between M and µ that would be expected if H0 was true
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis?
A sample mean much different than 80 with α = .05
A sample of n = 9 scores has a variance of s2 = 36. What is the estimated standard error for the sample mean?
2
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, what is the correct statistical decision?
Fail to reject H0
A sample of n = 4 scores is obtained from a population with μ = 70 and σ = 8. If the sample mean corresponds to a z-score of 2.00, what is the value of the sample mean?
M= 78
A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores. The hypothesis test produces a z-score of z = 2.27. If the researcher is using a one-tailed test, what is the correct statistical decision?
Reject the null hypothesis with α = .05 but not with α = .01
A hypothesis test involves a comparison of which two elements? a. Research results from a sample and a hypothesis about a population b. Research results from a population and a hypothesis about a sample c. Research results from a population and a hypothesis about the population d. Research results from a sample and a hypothesis about the sample
Research results from a sample and a hypothesis about a population
What is measured by the numerator of the z-score test statistic? a. A likely distance between M and µ that would be expected if H0 was true b. The actual distance between M and µ c. The position of the sample mean relative to the critical region d. Whether or not there is a significant difference between M and µ
The actual distance between M and µ
Why are t statistics more variable than z-scores?
The extra variability is caused by variations in the sample variance
Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then what is the relationship between the two t values?
The sample with the smaller variance will produce the larger t statistic
T/F: According to the central limit theorem, the standard error for a sample mean becomes smaller as the sample size increases.
True
Which set of characteristics will produce the smallest value for the estimated standard error?
a large sample size and a small sample variance
What is the effect of decreasing the alpha level (for example, from α = .05 to α = .01)?
all of the other options are results of decreasing alpha
By selecting a larger alpha level, a researcher is ______.
all of the other options are the results of selecting a larger alpha level
Which of the following accurately describes 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
an inferential technique that uses the data from a sample to draw inferences about a population
With a = .05, how are the boundaries for the critical region determined?
boundaries are drawn so there is 2.5% (.025) in each tail of the distribution.
What is the consequence of a Type II error?
concluding that a treatment has an effect when it really does
What is the consequence of a Type I error?
concluding that a treatment has an effect when it really has no effect
A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?
d= 0.50
T/F: If a hypothesis test rejects the null hypothesis using an alpha level of α = .05, then the research report would include the statement, "p > .05."
false
When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?
it is flatter and more spread out than the normal distribution
If other factors are held constant, what is the effect of increasing the sample size?
it will decrease the estimated standard error and increase the likelihood of rejecting H0
A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 30, how many individuals were in the sample?
n= 31
Which of the following accurately describes the critical region? a. Outcomes with a very low probability if the null hypothesis is true b. Outcomes with a high probability if the null hypothesis is true c. Outcomes with a very low probability whether or not the null hypothesis is true d. Outcomes with a high probability whether or not the null hypothesis is true
outcomes with a very low probability if the null hypothesis is true
A two-tailed hypothesis is being used to evaluate a treatment effect with a = .05. If the sample data produce a z-score of z = -2.24, what is the correct decision?
reject the null hypothesis and conclude that the treatment has an effect
What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72?
s2 = 9 and sM = 1
Which of the following is directly addressed by the null hypothesis for a population? a. The population before treatment c. The sample before treatment b. The population after treatment d. The sample after treatment
the population after treatment
A sample of n = 25 individuals is selected from a population with µ = 80, and a treatment is administered to the sample. What is expected if the treatment has no effect?
the sample mean after the treatment should be very different from 80 and should lead you to reject the null hypothesis.
What is the standard error of M?
the standard deviation of the distribution of sample means
If a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the t statistic?
the t statistic does not require any information about the population
Which of the following is a fundamental difference between the t statistic and a z-score? a. The t statistic uses the sample mean in place of the population mean. b. The t statistic uses the sample variance in place of the population variance. c. The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n. d. All of these are differences between t and z.
the t statistic uses the sample variance in place of the population variance
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (H0) say about the treatment?
the treatment has no effect on the scores
Which of the following is not needed to compute a t statistic? a. A hypothesized value for the population mean b. The value of the population variance or standard deviation c. The value of the sample mean d. The value of the sample variance or standard deviation
the value of the population variance or standard deviation
T/F: Compared to a z-score, a hypothesis test with a t statistic requires more information from the sample
true
T/F: If a hypothesis test leads to rejecting the null hypothesis, it means that the sample data failed to provide sufficient evidence to conclude that the treatment has an effect.
true
T/F: If the research prediction is that the treatment will decrease scores, then the critical region for a directional test will be in the left-hand tail.
true
T/F: In general, the null hypothesis states that the treatment has no effect on the population mean.
true
T/F: It is possible for a very small treatment effect to be a statistically significant treatment effect.
true
T/F: When the population variance or standard deviation is not known, you must use a t statistic instead of a z-score for a hypothesis test.
true
You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually has no effect, which of the following is true?
you have made a type I error
You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to fail to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true?
you have made the correct decision
A sample of n = 16 scores is obtained from a population with μ = 50 and σ = 16. If the sample mean is M = 54, then what is the z-score for the sample mean?
z= 1.00
