Quiz 15.1
Under what circumstances can a very small treatment effect still be significant?
A large sample size allows small effects to be detected.
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, then what is the correct decision?
A two-tailed test with alpha level 0.05 has the z-score cut-off as +/-1.96. Therefore, a z-score of 2.24 is beyond the cut-off point, is highly unlikely to be randomly occurring , and therefore the null hypothesis can be rejected.
Decreasing the alpha level from α = .05 to α = .01 ____.
Decreasing the alpha level decreases your chance of rejecting the null, but it also decreases the chance of Type I error.
A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population which is known to have a mean of μ = 80. The results will be examined using a one-tailed hypothesis test. Which of the following is the correct statement of the null hypothesis?
If the population mean score is 80 and your hypothesis is that the treatment will INCREASE the score, then a sample score equal or less than 80 would be part of the null.
Which of the following correctly describes the effect of increasing the alpha level (for example, from .01 to .05)?
Increasing the alpha level increases your chance of rejecting the null, but it also increases the chance of Type I error.
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?
Larger alpha level and a more different sample mean will result in higher likelihood of rejecting the null
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?
Look at the the z-formula on GW page 243. To have a more extreme z-value, you would want a large numerator and a small denominator. To get a large numerator, you would want a sample mean very different from the population mean. To get a small denominator, you would want a large sample size.
A researcher expects a treatment to produce an increase in the population mean. The treatment is evaluated using a one tailed hypothesis test, and the test produces z = +1.85. Based on this result, what is the correct statistical decision?
Refer to the z-table to find the appropriate z-score. A 0.05 in tail corresponds to z of 1.65 and a 0.01 in tail corresponds to a z of 2.33. Therefore, a z-score of 1.85 is enough to reject the null if alpha=0.05 but not if alpha=0.01.
Which of the following accurately describes the effect of increasing the sample size?
See the formula on GW page 243. Increasing sample size decreases the standard error. Because Type I error risk is set by alpha level and the sample size does not change the alpha level, Type I error risk is not affected.
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, given the same alpha level, which combination of factors is most likely to result in rejecting the null hypothesis?
To reject the null, you would want a more extreme z-score. Look at the formula on GW page 243. A combination of small standard deviation and large sample size would produce the smallest standard error and consequently the most extreme z-score.