statistics
posted by Lily on .
Can someone please explain to me the procedures for getting an answer to the questions. Step by step would be great since I'm very confused. I know it's probably simple.
* Numerous studies have demonstrated that listening to music while studying can improve memory. To demonstrate this phenomena, a researcher obtains a sample of college students and gives them a standardized memory test while they are listening to background music. under normal circumstances(without music), the scores on the test form a normalshaped distribution with a mean of lower case mu 25 and a standard deviation of lower case sigma 6. The sample produces a mean score of M=28.
a)If the sample consists of n=4 students, is this result sufficient to conclude that music had a significant effect on memory scores? Use a twotailed test with alpha level=.05
b) If the sample consists of n=36 students, is this result sufficient to conclude that the music had a significant event? Again, use a two test with alpha level= .05.

Both parts are using onesample twotailed tests. Since the sample in part a) is so small, you can try a onesample ttest and for part b), a onesample ztest.
For the ttest:
tstatistic = (sample mean  population mean)/(standard deviation divided by the square root of the sample size)
Ho: µ = 25 >null hypothesis
Ha: µ does not equal 25 >alternate hypothesis
You can finish this calculation:
tstatistic = (28  25)/(6/√4)
Using a ttable at 0.05 level of significance for a twotailed test (alternate hypothesis does not show a specific direction) at 3 degrees of freedom (df = n  1 = 4  1 = 3), look for the value and remember it could be + or  that value because the results could be in either tail of the distribution.
Does the test statistic exceed the negative or positive critical or cutoff value from the ttable? If it does, the null is rejected in favor of the alternate hypothesis and you can conclude a significant difference. If it does not, then you cannot reject the null and conclude a difference.
For the ztest, everything is basically the same (even the formula), except for the sample size and using the ztable instead of a ttable. Here's a hint: for a twotailed test at alpha level .05 , the cutoff values are +/1.96 using a ztable.
I hope this will help get you started.