Stats Chapter 8
You read about a study testing whether night shift workers sleep the recommended 8 hours per day. Assuming that the population variance of sleep (per day) is unknown, what type of t test is appropriate for this study?
one-sample t test
The ________ is an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis.
t statistic
A researcher conducts two t tests. Test 1 is a one-tailed test with a smaller sample size at a .05 level of significance. Test 2 is a one-tailed test with a larger sample size at a .05 level of significance. What do you know about the critical values for each test?
Test 2 is associated with smaller critical values.
In a sample of 20 participants, a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error (SM) of 1.6. What is the lower confidence limit for this interval?
2.1
A researcher selects a sample of 32 participants who are assigned to participate in a study with one group. What are the degrees of freedom for this test?
31
A researcher reports with 90% confidence that 31% to 37% of Americans believe in ghosts. What is the point estimate for this interval?
34%
To compute a one-sample t test, a researcher has to know many values. Which of the following is NOT a value that the researcher must know to compute this test?
The population variance must be known.
State the critical value(s) for the following two-tailed t test at a .05 level of significance: t(∞).
both b and c (±1.96; the same as for a two-tailed z test at a .05 level of significance)
A researcher conducts a study measuring comparing the obesity rate in a small community to the known obesity rate in the United States. Assuming that the population variance in unknown, what type of t test is appropriate for this study?
one-sample t test
The estimated standard error in the t statistic uses the ________ to estimate the ________ when the population variance is unknown.
sample variance; population variance
Is a one-sample t test reported differently for one-tailed and two-tailed tests?
No, the same values are reported
As a requirement for the t test, researchers compute any type of t test with samples selected from populations in which
the population variance is unknown
In a sample of 12 participants, a researcher estimates the 80% CI for a sample with a mean of M = 22.3 and an estimated standard error (SM) of 4.7. What is the confidence interval at this level of confidence?
80% CI 15.9, 28.7
Two researchers (A and B) compute a one-sample t test. For both tests, the standard error is the same, but the mean difference between the sample and value stated in the null hypothesis is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?
Researcher B
A key difference between a t statistic and a z statistic is that the standard error is ________ to compute a t statistic.
estimated
A researcher reports a significant effect with t(14) = 3.24. Compute eta-squared for this result.
n2 = 0.43 (large effect size)
Which of the following summarizes a t test that was significant and associated with a large effect size?
t(12) = 2.95, p < .05, d = .82
A researcher reports that college students consume an average of 3.6 alcoholic drinks per week. What is the interval estimate in this example?
the interval estimate is not given
Which of the following best describes the goal of estimation?
to narrow in on the true population mean by defining limits within which it is likely to be contained
In a sample of 20 participants, a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error (SM) of 1.6. What is the upper confidence limit for this interval?
8.8
In a sample of 28 participants, a researcher estimates the 95% CI for a sample with a mean of M = 1.5 and an estimated standard error (SM) of 0.3. What is the confidence interval at this level of confidence?
95% CI 0.9, 2.1
The t distribution is similar to the z distribution except
All of the above (it is associated with greater variability; it is characterized by "thicker" tails compared with the z distribution; it is associated with scores being more likely in the tails of the distribution)
It is most appropriate to report effect size with a significant result. Why is it generally inappropriate to report effect size with insignificant results?
Because it makes little sense to report the size of an effect that you just concluded doesn't exist.
Which of the following explains why point estimation can be a useful procedure to estimate a population mean?
Both b and c (The sample mean is equal to the population mean on average.; The sample mean is an unbiased estimator of the population mean.)
Which type of error is used to compute the confidence interval for one sample selected from a population with an unknown variance?
estimated standard error
A researcher reports a significant effect in some population. If he computes both an eta-squared and an omega-squared effect size estimate, then which estimate will be the largest?
eta-squared
Which measure of effect size is most commonly reported with a t test?
Cohen's d
State the critical value(s) for a t test using a .05 level of significance in the lower tail only: t(24).
-1.711
Computing a one-sample t test is appropriate when
All of the above - when the population variance is unknown; participants are assigned to only one group; and participants are observed at one time
A point estimate is typically reported with an interval estimate. Why?
All of the above -Using only a point estimate is associated with low certainty.; The interval estimate gives researchers a higher level of confidence.; The interval estimate adds certainty to the estimate of the population mean.
Which of the following is an assumption for computing any type of independent sample t test?
All of the above- Data in the population being sampled are normally distributed.; Data were obtained from a sample that was selected using a random sampling procedure.; The probabilities of each measured outcome in a study are independent.
Two researchers (A and B) compute a one-sample t test. For both tests, the mean difference between the sample and value stated in the null hypothesis is 5, but the standard error is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?
Researcher A
A researcher conducts a study and concludes that a new behavioral health treatment program significantly reduces one's risk for disease compared with risk levels in the general population (d = -0.64). Interpret the size of this effect.
Risk levels in the population shifted 0.64 standard deviations below the mean.
A statistical procedure in which a sample statistic is used to estimate the value of an unknown population parameter is called
estimation
A researcher reports that stress levels among nurses are higher compared to stress levels in the general population, t(20) = 2.086, p = .05 (d = .12). Was this a one-tailed or a two-tailed test?
a two-tailed test because the p value is equal to .05
A researcher conducts two t tests. Test 1 is a two-tailed test with a smaller sample size at a .05 level of significance. Test 2 is a two-tailed test with a larger sample size at a .05 level of significance. What do you know about the degrees of freedom for each test?
Test 2 is associated with larger degrees of freedom.
A researcher reports that the mean time it takes to complete an experimental task is 1.4±8.0 (M±SD) seconds. If the null hypothesis was that the mean equals 1.0, then what is the effect size for this test using estimated Cohen's d?
d = 0.05; small effect size
A professor compares final exam scores in his psychology class to final exam grades in another comparable professor's class. Assuming that the population variance of exam scores is unknown, what type of t test is appropriate for analyzing differences between these classes?
two-independent sample t test
State the critical value(s) for a t test using a two-tailed test at a .05 level of significance: t(20).
±2.086
The mean crying time of infants during naptime at a local preschool is 12 minutes. The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8±4.6 (M±SD) minutes. Test whether this new naptime routine reduced crying time at a .05 level of significance.
The new naptime routine significantly reduced crying time, t(24) = -4.35, p < .05.
A local elementary school determined that the average number of volunteers for their "Step into Spring" annual fundraiser has been 14 persons on average (per event). After taking additional measures to recruit volunteers this year, they got 28 people to volunteer. Test whether these additional measures increased the number of volunteers at a .05 level of significance.
There is not enough information to answer this question.
The average response time to a bank robbery is about 9 minutes. A local community wants to improve on this time, so they implement advanced training seminars. They find that the new response time for a sample of 36 police officers is 8±4.2 (M±SD) minutes. Test whether this advanced training seminar reduced response time at a .05 level of significance.
This advanced training seminar did not reduce response time, t(35) = -1.43, p > .05.
A researcher selects a sample of 16 women and asks them to rate how important a sense of humor is in someone they want a long-term relationship with. She records scores averaging 1.6±0.8 (M±SD) on a rating scale from -3 (not important at all) to +3 (very important). Assuming that an average score of 0 is the null hypothesis, test whether or not women find this trait important at a .05 level of significance.
Women found this trait to be important, and this result was significant, t(15) = 8.00, p < .05.
A researcher reports that mean ratings of liking for some food are 0.8±2.4 (M±SD). If the null hypothesis was that the mean equals 0, then what is the effect size for this test using estimated Cohen's d?
d = 0.33; medium effect size
A researcher records the number of distracters (such as noises) that preschool-aged children ignore while watching a popular Sunday morning cartoon show. Assuming that the population variance is unknown, what type of t test is appropriate for this study?
one-sample t test