PSY 555 Homework 10
Chapter 5: #17,18,27,28
5.17(a). Mean ADDSC score for boys=54.29, s=12.90 [calculated from the Data Set]
Since a score of 50 is below the mean, and since we are looking for the probability of a score greater than 50, we want to look in the tables of the normal distribution in the column labeled, "larger portion."
5.17(b). (Notice that one percentage refers to the proportion greater than 50, while the other refers to the proportion greater than or equal to 50).
5.18. p(that person will drop out of school, given that he/she has an ADDSC of at least 60)=
5.27. Number of subjects needed in Exercise 5.26's verbal learning experiment if each subject can see only two of the four classes of words.
5.28. Chance that a subject will press correctly on first trial when learning to press three out of five buttons in a certain order:
There are 60 possible orders to push 3 out of 5 buttons. The probability that the subject will choose the correct order on the first trial=p()=.017.
The researcher has lost 21 pairings of pictures.
There is a .0089 probability of getting a score of 110 or greater.
3. The central limit theorem essentially says that, regardless of the shape of the population distribution, as n increases, the sampling distribution of the means approaches normality and the rate at which the sampling distribution approaches normality is a function of how normally the actual population is distributed. Furthermore, the standard deviation of the sampling distribution of the means (the standard error of the means) equals This theorem is important because it allows us to use the normal distribution to assess probability, regardless of the shape of the original distribution. We should be aware, however, that the sampling distribution of s may not be normal, and therefore, the central limit theorem is not a panacea for non-normal distributions.
4. Estimates of parameters can be based upon different amounts of information. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom (df). In general, the degrees of freedom of an estimate is equal to the number of independent scores that go into the estimate minus the number of parameters estimated as intermediate steps in the estimation of the parameter itself. For example, if the variance, σ2 , is to be estimated from a random sample of N independent scores, then the degrees of freedom is equal to the number of independent scores (N) minus the number of parameters estimated as intermediate steps (one, μ is estimated by M) and is therefore equal to N-1.
5. The t-distribution begins to approach the z-distribution, or normality, as N approaches infinity because as N increases, the noise in your sample estimates (s as an estimate of s) is reduced. The t-distribution is a special distribution that is essentially the same as the z-distribution with one important difference--the t-distribution, unlike the z-distribution, accounts for the sample error of the standard deviation. So, as the sample error for the standard error is minimized (which occurs the more N increases), the t-distribution has less error to account for and approaches the z-distribution, which is normal.