In the Chapter Preview we described a study showing that students had more academic problems following nights with less than average sleep compared to nights with more than average sleep (Gillen-O’Neel, Huynh, & Fuligni, 2013). Suppose a researcher is attempting to replicate this study using a sample of n = 8 college freshmen. Each student records the amount of study time and amount of sleep each night and reports the number of academic problems each day. The following data show the results from the study 1. Treat the data as if the scores are from an independent-measures study using two separate samples, each with n = 8 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? 2.Now assume that the data are from a repeatedmeasures study using the same sample of n = 8 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference and the repeated-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? (You should find that the repeated-measures design substantially reduces the variance and increases the likelihood of rejecting H0 .)
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
In the Chapter Preview we described a study showing that students had more academic problems following nights with less than average sleep compared to nights with more than average sleep (Gillen-O’Neel, Huynh, & Fuligni, 2013). Suppose a researcher is attempting to replicate this study using a sample of n = 8 college freshmen. Each student records the amount of study time and amount of sleep each night and reports the number of academic problems each day. The following data show the results from the study
1. Treat the data as if the scores are from an independent-measures study using two separate samples, each with n = 8 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores?
2.Now assume that the data are from a repeatedmeasures study using the same sample of n = 8 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference and the repeated-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? (You should find that the repeated-measures design substantially reduces the variance and increases the likelihood of rejecting H0 .)
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