- Questions
math
*The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all
other variables are held constant, explain how the value of z is influenced by each of the following:
a. Increasing the difference between the sample mean
and the original population mean.
b. Increasing the population standard deviation.
c. Increasing the number of scores in the sample.
*If the alpha level is changed from _ _ .05 to _ _ .01,
a. What happens to the boundaries for the critical
region?
b. What happens to the probability of a Type I error?
*Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). In a representative study, a sample of n _ 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of __40 and a standard deviation of _ _ 12. The sample of group-participation adolescents had an average of M _ 43.84.
a. Does this sample provide enough evidence to
conclude that self-esteem scores for these adolescents
are significantly different from those of the general
population? Use a two-tailed test with _ _.01.
b. Compute Cohen’s d to measure the size of the
difference.
c. Write a sentence describing the outcome of the
hypothesis test and the measure of effect size as it
would appear in a research report.
* A random sample is selected from a normal population with a mean of _ _ 50 and a standard deviation of _ _ 12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M _ 55.
a. If the sample consists of n _ 16 scores, is the
sample mean sufficient to conclude that the
treatment has a significant effect? Use a two-tailed test with _ _ .05.
b. If the sample consists of n _ 36 scores, is the
sample mean sufficient to conclude that the
treatment has a significant effect? Use a two-tailed test with _ _ .05.
c. Comparing your answers for parts a and b, explain
how the size of the sample influences the outcome
of a hypothesis test.
*Miller (2008) examined the energy drink consumption of college undergraduates and found that males use
energy drinks significantly more often than females. To further investigate this phenomenon, suppose that
a researcher selects a random sample of n _ 36 male undergraduates and a sample of n _ 25 females. On average, the males reported consuming M _ 2.45 drinks per month and females had an average of M _ 1.28. Assume that the overall level of consumption for college undergraduates averages _ _ 1.85 energy drinks per month, and that the distribution of monthly consumption scores is approximately normal with a standard deviation of _ _ 1.2. a. Did this sample of males consume significantly more energy drinks than the overall population average? Use a one-tailed test with _ _ .01.
*Did this sample of females consume significantly
fewer energy drinks than the overall population
average? Use a one-tailed test with _ _ .01
*There is some evidence that REM sleep, associated with dreaming, may also play a role in learning and
memory processing. For example, Smith and Lapp (1991) found increased REM activity for college
students during exam periods. Suppose that REM activity for a sample of n _ 16 students during the
final exam period produced an average score of M _ 143. Regular REM activity for the college
population averages _ _ 110 with a standard deviation of _ _ 50. The population distribution is approximately normal.
a. Do the data from this sample provide evidence for a significant increase in REM activity during exams?
Use a one-tailed test with _ _ .01.
b. Compute Cohen’s d to estimate the size of the
effect.
c. Write a sentence describing the outcome of the
hypothesis test and the measure of effect size as it
would appear in a research report.
* A psychologist is investigating the hypothesis that children who grow up as the only child in the household develop different personality characteristics than those who grow up in larger families. A sample of n _ 30 only children is obtained and each child is given a standardized personality test. For the general population, scores on the test from a normal distribution with a mean of _ _ 50 and a standard deviation of _ _ 15. If the mean for the sample is
M _ 58, can the researcher conclude that there is a significant difference in personality between only
children and the rest of the population? Use a twotailed test with _ _ .05.
* Montarello and Martins (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with
a mean of _ _ 100 and a standard deviation of _ _ 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions, and gives the modified test to a sample of n _ 36 students. If the average test score for the sample is M _ 104, is this result sufficient to conclude that inserting the easy questions improves
student performance? Use a one-tailed test with _ _ .01.
* A researcher plans to conduct an experiment testing the effect of caffeine on reaction time during a driving simulation task. A sample of n _ 9 participants is selected and each person receives a standard dose of caffeine before being tested on the simulator. The caffeine is expected to lower reaction time by an average of 30 msec. Scores on the simulator task for the regular population (without caffeine) form a normal distribution with _ _ 240 msec. and _ _ 30.
a. If the researcher uses a two-tailed test with _ _ .05,
what is the power of the hypothesis test?
b. Again assuming a two-tailed test with _ _ .05,
what is the power of the hypothesis test if the
sample size is increased to n _ 25?
* Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant.
a. The size of the z-score in a hypothesis test.
b. The size of Cohen’s d.
c. The power of a hypothesis test.
* A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals
with systolic pressure greater than 140. For this population, systolic scores average _ _ 160 with a standard deviation of _ _ 20, and the scores form a normal-shaped distribution. The researcher plans to select a sample of n _ 25 individuals, and measure their systolic blood pressure after they take the medication for 60 days. If the researcher uses a two-tailed test with _ _ .05,
a. What is the power of the test if the medication has
a 5-point effect?
b. What is the power of the test if the medication has
a 10-point effect?