*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?
my questions still have not been answered, I need b4 midnite central time almost that time
a. Increasing the difference between the sample mean and the original population mean:
When you increase the difference between the sample mean and the original population mean, the value of the z-score will also increase. The z-score measures how many standard deviations the sample mean is away from the population mean. When the difference between the sample mean and population mean is larger, it indicates a greater deviation from the expected value, leading to a larger z-score.
b. Increasing the population standard deviation:
Increasing the population standard deviation will also increase the value of the z-score. The z-score is calculated by taking the difference between the sample mean and the population mean and dividing it by the standard deviation of the population. When the standard deviation is larger, it indicates a greater spread of the data points around the population mean, leading to a larger z-score.
c. Increasing the number of scores in the sample:
Increasing the number of scores in the sample will decrease the value of the z-score. The z-score is calculated by taking the difference between the sample mean and the population mean and dividing it by the standard deviation of the population, which is also influenced by sample size. As the sample size increases, the standard deviation of the sample mean decreases, resulting in a smaller z-score.
If the alpha level is changed from .05 to .01:
a. The boundaries for the critical region will become more strict or narrow. The critical region represents the range of z-scores that would lead to rejecting the null hypothesis. By changing the alpha level to .01, it means that the researcher wants to reduce the chance of a Type I error (incorrectly rejecting the null hypothesis) and therefore the critical region becomes narrower.
b. The probability of a Type I error will decrease. A Type I error occurs when the null hypothesis is rejected even though it is true. By reducing the alpha level from .05 to .01, the researcher is lowering the threshold for rejecting the null hypothesis and becoming more conservative in making conclusions. This decrease in the alpha level reduces the probability of committing a Type I error.
For the other questions, please provide the values for the missing information such as the hypothesized mean, sample mean, sample size, standard deviation, etc.
a. Increasing the difference between the sample mean and the original population mean:
When the difference between the sample mean and the original population mean increases, it means that the sample mean is further away from the population mean. This will result in a larger z-score, indicating a larger deviation from the population mean.
b. Increasing the population standard deviation:
Increasing the population standard deviation will increase the variability within the population. With a higher standard deviation, the z-score will be smaller for a given sample mean, indicating a smaller difference from the population mean.
c. Increasing the number of scores in the sample:
Increasing the number of scores in the sample will result in a more reliable estimate of the population mean. With a larger sample size, the standard error of the mean decreases, which leads to a smaller z-score for a given difference between the sample mean and the population mean.
If the alpha level is changed from 0.05 to 0.01:
a. The boundaries for the critical region become more stringent. This means that it becomes more difficult to reject the null hypothesis as the critical values for the test statistic become more extreme.
b. The probability of a Type I error decreases. A Type I error occurs when the null hypothesis is rejected when it is actually true. With a lower alpha level (0.01), the probability of making a Type I error is reduced.
For the hypothesis test comparing self-esteem scores of adolescents in a group participation sample to the general population:
a. To determine if the sample provides enough evidence to conclude that the self-esteem scores are significantly different from the general population, a two-tailed test is conducted with an alpha level of 0.01. The null hypothesis would state that there is no significant difference between the sample mean (M = 43.84) and the population mean (μ = 40), while the alternative hypothesis would state that there is a significant difference.
b. Cohen's d can be computed using the formula: d = (M - μ) / σ, where M is the sample mean, μ is the population mean, and σ is the population standard deviation. In this case, the difference between the sample mean (M = 43.84) and the population mean (μ = 40) is divided by the population standard deviation (σ = 12) to obtain the value of Cohen's d.
c. The outcome of the hypothesis test would be described in the research report, stating whether the null hypothesis is rejected or not at a significance level of 0.01. The measure of effect size, Cohen's d, would also be included in the report to indicate the magnitude of the difference between the sample mean and the population mean in terms of standard deviations.
For the treatment effect on the sample mean:
a. If the sample consists of n = 16 scores, a two-tailed test is conducted with an alpha level of 0.05. The null hypothesis would state that there is no significant effect of the treatment on the sample mean (M = 55), while the alternative hypothesis would state that there is a significant effect.
b. If the sample consists of n = 36 scores, the same two-tailed test with an alpha level of 0.05 is conducted. The null hypothesis would still state no significant effect, while the alternative hypothesis would state a significant effect.
c. The sample size influences the outcome of a hypothesis test by affecting the precision of the estimate. With a larger sample size, the standard error of the mean decreases, resulting in a smaller standard deviation and a more precise estimate of the population mean. This can increase the chance of finding a significant effect in the data.
For the comparison of energy drink consumption between males and the overall population average:
a. To determine if the sample of males consumed significantly more energy drinks than the overall population average, a one-tailed test is conducted with an alpha level of 0.01. The null hypothesis would state that there is no significant difference between the sample mean (M = 2.45) and the population mean (μ = 1.85), while the alternative hypothesis would state that the sample mean is significantly greater.
b. To compute Cohen's d, the difference between the sample mean (M = 2.45) and the population mean (μ = 1.85) is divided by the standard deviation of the population (σ = 1.2).
For the comparison of REM activity during exams:
a. To determine if there is a significant increase in REM activity during exams, a one-tailed test is conducted with an alpha level of 0.01. The null hypothesis would state that there is no significant increase in REM activity, while the alternative hypothesis would state that there is a significant increase.
b. To compute Cohen's d, the difference between the sample mean (M = 143) and the population mean (μ = 110) is divided by the population standard deviation (σ = 50).
The outcome of the hypothesis test and the measure of effect size (Cohen's d) would be described in a research report, stating whether the null hypothesis is rejected or not at a significance level of 0.01 and indicating the magnitude of the effect in standard deviations.
For the investigation of personality differences between only children and the rest of the population:
To determine if there is a significant difference in personality between only children and the rest of the population, a two-tailed test is conducted with an alpha level of 0.05. The null hypothesis would state that there is no significant difference between the sample mean (M = 58) and the population mean (μ = 50), while the alternative hypothesis would state that there is a significant difference.
For the investigation of the effect of inserting easy questions on student performance:
To conclude if inserting easy questions improves student performance, a one-tailed test is conducted with an alpha level of 0.01. The null hypothesis would assume no improvement, while the alternative hypothesis would state that inserting easy questions leads to better performance.