Research Methods Test #2 Chapters 6-9
If a hypothesis test produces a z-score in the critical region, what decision should be made?
Reject the null hypothesis
Which of the following is a fundamental difference between the t statistic and a z-score?
The t statistic uses the sample variance in place of the population variance.
What proportion of a normal distribution is located in the tail beyond z = 1.50?
What proportion of a normal distribution is located in the tail beyond z = 1.50?
With α = .05, what is the critical t value for a one-tailed test with n = 15?
t = 1.761
According to the central limit theorem, the standard error for a sample mean becomes smaller as the sample size increases.
true
Which of the following accurately describes a hypothesis test?
An inferential technique that uses the data from a sample to draw inferences about a population
Which of the following is an accurate definition of a Type II error?
Failing to reject a false null hypothesis
Under what circumstances will the distribution of sample means be normal?
If the population is normal or if the sample size is greater than 30
What happens to the standard error of M as sample size increases?
It decreases
What is the expected value of M?
The mean of the distribution of sample means
What symbol is used to identify the standard error of M?
σM
A vertical line is drawn through a normal distribution at z = 0.80. What proportion of the distribution is on the right-hand side of the line?
0.2119
What proportion of a normal distribution is located between z = 0 and z = +1.50?
0.4332
A vertical line drawn through a normal distribution at z = 0.50 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body?
0.6915
A class consists of 10 male and 30 female students. If one student is randomly selected from the class, what is the probability of selecting a male student?
10/40
For a particular population, a sample of n = 4 scores has a standard error of 6. For the same population, a sample of n = 16 scores would have a standard error of _____.
3
If random samples, each with n = 9 scores, are selected from a normal population with µ = 80 and σ = 18, how much difference, on average, should there be between a sample mean and the population mean?
6
Which set of characteristics will produce the smallest value for the estimated standard error?
A large sample size and a small sample variance
A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 76?
0.6915
Which combination of factors will produce the largest value for the standard error?
A small sample and a large standard deviation
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
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.
Which of the following describes what a confidence interval does?
It uses a sample mean to estimate the corresponding population mean.
Which of the following accurately describes the critical region?
Outcomes with a very low probability if the null hypothesis is true
Which of the following is an accurate definition of a Type I error?
Rejecting a true null hypothesis
What is the standard error of M?
The standard deviation of the distribution of sample means
Which of the following will increase the power of a statistical test?
The treatment has no effect on the scores.
With α = .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.
IQ scores form a normal distribution with µ = 100 and σ = 15. Individuals with IQs above 140 are classified in the genius category. What proportion of the population consists of geniuses?
0.0038
What proportion of a normal distribution is located between the mean and z = 1.40
0.4192
What proportion of a normal distribution is located between z = -1.25 and z = +1.25?
0.7888
The results of a hypothesis test are reported as follows: t(15) = 2.70, p < .05. Based on this report, how many individuals were in the sample?
16
A sample of n = 4 scores has SS = 60. What is the variance for this sample?
20
Under what circumstances can a very small treatment effect be statistically significant?
If the sample size big and the sample variance is small
A sample of n = 25 scores produces a t statistic of t = 2.062. If the researcher is using a two-tailed test, which of the following is the correct statistical decision?
The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.
You complete a hypothesis test using α = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. Which of the following is true?
You might have made a Type I error, but the probability is less than 5%.
Which of the following is a requirement for a random sample? Every individual has an equal chance of being selected. a. Every individual has an equal chance of being selected b. The probabilities cannot change during a series of selections. c. There must be sampling with replacement d. All of the other 3 choices are correct.
d. all answers are correct
What happens to the expected value of M as sample size increases?
it stays constant
On average, what value is expected for the t statistic when the null hypothesis is true?
t=0