# Hypothesis Testing

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A statistician claims that the average score on a standardized test of students who major in psychology is greater than the average of students who major in mathematics. The results of the test, given to 50 students in each group, are shown below. Is there enough evidence to support the statistician's claim at a 1% level of significance?

psychology mathematics

X1 = 118 X2 = 115

s1 = 15 s2 = 15

n1 = 50 n2 = 50

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Define the null hypothesis H0:u1=u2;

H1:u1>u2.

We can use the statistic T=(X1-X2)/S where S^2=S1^2/n1+S2^2/n2. We compute that S^2=2*15^2/50, ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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