Stat in Behavioral Science Exam #2
What z-score value separates the highest 10% of the scores in a normal distribution from the lowest 90%?
z = 1.28
What symbol is used to identify the standard error of M?
σM
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
A normal distribution has μ = 20 and σ = 4. What is the probability of randomly selecting a score greater than 25 from this distribution?
0.1056
What proportion of a normal distribution is located in the tail beyond z = -1.00?
0.1587
A normal distribution has a mean of µ = 60 with σ = 8. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 54?
0.2734
If a hypothesis test is found to have power = 0.70, what is the probability that the test will result in a Type II error?
0.30
A vertical line drawn through a normal distribution at z = -1.00 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body?
0.8413
A vertical line drawn through a normal distribution at z = -1.00 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the tail?
0.8413
What is the probability of randomly selecting a z-score less than z = 1.25 from a normal distribution?
0.8944
A class consists of 10 male and 30 female students. A random sample of n = 3 students is selected. If the first two students are both females, what is the probability that the third student is a male?
10/38
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 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 ____. 5; 80
80; 5
What is measured by the denominator of the z-score test statistic?
A likely distance between M and µ that would be expected if H0 was true
A sample is obtained from a population with μ = 100 and σ = 20. Which of the following samples would produce the most extreme z-score? -A sample of n = 100 scores with M = 104 -A sample of n = 25 scores with M = 102
A sample of n = 100 scores with M = 104
Which of the following will increase the power of a statistical test? -Change the sample size from n = 25 to n = 100 -Change from a one-tailed test to a two-tailed test
Change the sample size from n = 25 to n = 100
What is the consequence of a Type I error?
Concluding that a treatment has an effect when it really has no effect
What is the consequence of a Type II error?
Concluding that a treatment has no effect when it really does
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 H1
Under what circumstances can a very small treatment effect still be significant?
If the sample size (n) is very large
For a normal population with µ = 40 and σ = 10 which of the following samples is least likely to be obtained? -M is less than 38 for a sample of n = 4 -M is less than 36 for a sample of n = 100
M is less than 36 for a sample of n = 100
For a normal population with µ = 40 and σ = 10, which of the following samples has the highest probability of being obtained? -M is less than 38 for a sample of n = 4 -M is less than 36 for a sample of n = 10
M is less than 38 for a sample of n = 4
Which of the following accurately describes the critical region? -Outcomes with a high probability if the null hypothesis is true -Outcomes with a very low probability if the null hypothesis is true
Outcomes with a very low probability if the null hypothesis is true
Which of the following accurately describes the proportions in the tails of a normal distribution? -Proportions in both tails are less than 0.50. -Proportions in both tails are greater than 0.50.
Proportions in both tails are less than 0.50.
A two-tailed hypothesis test is being used to evaluate a treatment effect with α = .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
A hypothesis test involves a comparison of which two elements?
Research results from a sample and a hypothesis about a population
What is measured by the numerator of the z-score test statistic?
The actual distance between M and µ
A random sample of n = 60 scores is selected from a population. Which of the following distributions will definitely be normal? -The distribution of sample means will definitely form a normal distribution. -The scores in the sample will definitely form a normal distribution.
The distribution of sample means will definitely form a normal distribution.
What is the expected value of M?
The mean of the distribution of sample means
Which of the following is an accurate definition for the power of a statistical test? -The probability of rejecting a false null hypothesis -The probability of supporting a false null hypothesis
The probability of rejecting a false null hypothesis
A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z = 2.37. Assuming that the researcher is using a two-tailed test, what decision should be made?
The researcher should reject the null hypothesis with α = .05 but not with α = .01.
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 close 80 and should lead you to fail to reject the null hypothesis.
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 alternative hypothesis (H1) say about the treatment?
The treatment causes a change in the scores.
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.
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
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis? σ = 10 and n = 25
σ = 5 and n = 50
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis?
σ = 5 and α = .05
Which of the following accurately describes the proportions in the body of a normal distribution? -Body proportions on the right side of the z-score are less than 0.50; on the left side, they are greater than 0.50. -Body proportions on either side of the z-score are greater than 0.50.
Body proportions on either side of the z-score are greater than 0.50.
A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 90 from this distribution?
0.1587
A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 80 and X = 100?
0.3413
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 greater than X = 58?
0.8413
For a particular population, a sample of n = 4 scores has an expected value of 10. For the same population, a sample of n = 25 scores would have an expected value of _____.
10
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 expected value for the sample mean?
40
If all the possible random samples, each with n = 6 scores, are selected from a normal population with μ = 72 and s = 8, and the mean is calculated for each sample, then what is the average value for all of the sample means?
72
Which of the following is a requirement for a random sample? -The probabilities cannot change during a series of selections. -There must be sampling with replacement. -Every individual has an equal chance of being selected.
All are requirements for a random sample
Seattle, Washington, averages 34 inches of annual precipitation. Assuming that the distribution of precipitation amounts is approximately normal with a standard deviation of 6.5 inches, determine which of the following represents an unusually rainy year.
Annual precipitation of 49.6 inches
All the possible random samples of size n = 4 are selected from a population with M = 37 and s = 10 and the mean is computed for each sample. Then all the possible samples of size n = 55 are selected from the same population and the mean is computed for each sample. How will the distribution of sample means for n = 4 compare with the distribution for n = 55?
The mean and variance for n = 55 will both be larger than the mean and variance for n = 4
If all the possible random samples of size n = 25 are selected from a population with M = 80 and s = 10 and the mean is computed for each sample, then what shape is expected for the distribution of sample means?
The sample means tend to form a normal-shaped distribution
What is the law of large numbers?
the larger the sample size (n), the more likely the sample mean will be close to the population mean
