What does the symbol n mean in psychology

What does psychology symbol ∑x^2 and (∑x)^2 mean??

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the first one is the sum of the x^2 and the second is (the sum of the x) ^2

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The Psychology department is interested in seeing if there was a significant difference in the mean lifesp?

Q: 1. The Psychology department is interested in seeing if there was a significant difference in the mean lifespan of psychology majors who earned a BA and those who earned a Ph. D. The department collected information from two random samples listed belowB.A.Ph. D. = 67.93 = 72.60S2 = 10.32S2 = 17.08n = 87n = 15Conduct an independent samples (2 sample) t-test using alpha = .05.STEP 1: State the null and alternative hypotheses in words (2 points) State the null and alternative hypotheses in symbols. (2 points)STEP 2: Set up the criteria for making a decision. That is, find the critical value. (1 point)STEP 3: Compute the appropriate test-statistic. Show your work! (3 points)STEP 4: Evaluate the null hypothesis (based on your answers to the above steps). (1 point)STEP 5: Based on your evaluation of the null hypothesis, what is your conclusion?(1 point)

A: I will answer it, as it gives me good practice for my upcoming statistics course but I recommend you consult the text book and go through this one you posted as they go through the process step by step and better explain things than I do here (and I may have missed a step or miscalculated something :)). My text helped me through my first statistics course :)Let me know if you agree if you do it all yourself. STEP 1Research Hypothesis: There is a difference of lifespans between those who get a B.A or a PH.DB.A does not equal (use the does not equal symbol here) Ph.DNull Hypothesis: There is no difference between the two.B.A = Ph.DSTEP 2Find the degrees of freedom first, so to do that you add the two N values (87 and 15) and subtract 2. So 102 – 2 = 100.Then look at the t table for a two tailed distribution, using the alpha of 0.05 and at 100 degrees freedom, you find the critical value to be 1.984 so:Critical Value = 1.984 (+ or -)STEP 3To find the test statistic we first have to calculate what is called the pooled estimate of the population variance. To do that we take the degrees of freedom for each group, divide that by the total degrees of freedom and multiply each by the variance of each group and add them together.So degrees of freedom for each group = (87 – 1) and (15 – 1)Degrees of freedom total we know is 100.So (86 / 100) * 10.32 = 8.8752 and (14 / 100) * 17.08 = 2.3912.Then 8.8752 + 2.3912 = 11.2664The we have to find the variance of each of the two distributions means so we do that by using the pooled estimate and dividing that by the number of participants in each group.So for group 1 it is (11.2664 / 87) = 0.129498851For group 2 it is (11.2664 / 15) = 0.751093333Then we find the variance and standard deviation of the distribution of differences between means. To find the variance we just add the two above.So the variance is equal to 0.751093333 + 0.129498851 = 0.880592184.The standard deviation is the square root of this value so it is 0.938398734.All the above was to get the standard deviation above so that we can calculate the actual test statistic.So to do that we take the mean of the B.A sample, subtract the Ph.D mean from it, and divide that total by the standard deviation above.So 67.93 – 72.60 = – 4.67- 4.67 / 0.938398734 = – 4.98 (rounded to 2 decimal places).STEP 4The null hypothesis is rejected because t = – 4.97 and is greater than the critical value of -1.984STEP 5Since we have rejected the null hypothesis, we can conclude that there is a significant difference between the mean lifespan of those with a B.A and those with a PH.D.