# Project #3900 - Statistics

IMPORTANT, BEFORE YOU START ANY CALCULATION, DECIDE WHICH TEST STATISTIC YOU ARE GOING TO USE. Feel free to e Mail me after you decide which test statistic you are going to use, I will let you know which statistic you should be using. This test statistic check has two purposes:  It will save you lots of unnecessary calculation and frustration if you are wrong, and second, it will give you some practice about matching the right test stat to the kind of problem you are solving.  Remember the possible test statistics we have studied so far include the Z test statistic, and the Single sample t, the independent samples t, and the repeated measures (dependent samples)  t.  Ha! I wonder if we have 4 different problems because we have 4 different test statistics.   Also, remember that when we use Z we MUST know σ , If we do not know σ  , then we have to estimate it from the sample data, and use a t test. .

FIRST   --   For each of the following, first decide which test statistic you should use to test the hypothesis. Then check with me, or if you feel confident, go to the next sterp.

SECOND   Carry out the analysis. Follow the step by step  hypothesis testing procedure, including the Null and alternative hypotheses,  showing the comparison distribution, where the cut-off (or critical region) is, what your obtained test statistic is, and whether you would reject  or accept the Null .

THIRD   for any problem in which you used a t test to test the hypothesis, carry out the same analysis using SPSS .  The results should match and it is a good way to check your calculations.

FOURTH   E mail your solutions, including each of the step in the hypothesis testing procedure, AND the print out of the spss results for each of the t test problems.  If you have a problem scanning or emailing me the spss results, I only need the following calculations for each spss t test---  The calculated mean difference or the sample mean,   the t value, and the p (or significance value).

1 A psychologist wants to know the relationship between depression and aging.  It is known that the general population averages µ = 40 on a standardized depression test(higher scores indicate more depression). The psychologist obtains a sample of 5 individuals who are over 70 and administers the test.  Their scores are:  42, 40, 43, 42, and 43.  On the basis of this sample, can the psychologist conclude that depression for elderly people is different from depression in the general population?  Use the .05 level.

(t-test for single sample?)

2  Some studies have shown that listening to music while studying can improve  memory. A researcher obtained a sample of six students and administered a standard memory test while the students were listening to background music.  Under normal conditions, ie, without music, µ = 20 and σ = 3.  Scores for the 6 students were:  18, 20, 23, 24, 24, 25. Can the researcher conclude that playing music improved the students’ memory for the material? Use the .05 level.

(z test?)

3  A teacher was interested in why some children who dressed neatly seemed to do better in school., that is their grades seemed better than children who dressed a bit less neatly. The teacher wondered whether the child’s ability was being graded, or whether the child’ s clothes somehow affected grades. She asked a few other teachers and parents to help in a study, but without telling them too much about the purpose of the study. She selected a sample of 10 students at the beginning of the school year and before their first class each day they spent a few minutes with teachers who “spruced them up” including combing/brushing hair, new or clean clothes, and whatever else was necessary to improve their appearance. She selected a second group who also met with a few teachers, who “unspruced” the children before classes started by letting them play a game which had the effect that their hair was not as neat, their clothes were a bit wrinkled, perhaps even smudges of dirt.  The teacher then checked the grades at the end of the first marking period and found that the “spruced up” kids’ scores were:  88, 78, 80, 92, 94, 78, 89, 93, 90, and 85.  The grades for the “unspruced” kids were:  90, 86, 87, 91, 77, 78, 73, 78, 83, and 87. What can the teacher conclude about whether “spruced up” kids do better than “unspruced” kids?  Use the .01 level.

T test for dependent?

4 Recent research is suggesting that exercise has a positive effect on cognition, and is even suggesting that exercise promotes the production of a “brain derived neurotrophic factor” better known as BDNF, which can help promote cell growth. There is considerable optimism that BDNF may be able to delay or even prevent the onset of Alzheimer’s, a particularly difficult and growing problem as the population ages. A team of researchers is examining the influence of BDNF. One member of the team has been assigned the task of researching the relation between BDNF production, exercise,   and gender. She selects a random sample of 5 females and measures the amount of  BDNF in the bloodstream after a week of relatively low physical activity. The amounts are .20 mg, .25, .30, .26, and .24.  She then arranges a week of moderate physical activity for the sample and measures the amount of BDNF. The amounts found(in the same order) are .24, .25, .33, .28, and .25. what conclusions should she reach about the effect of exercise and BDNF in women? Use the .05 level.

 Subject Mathematics Due By (Pacific Time) 04/04/2013 12:00 am
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