X. The random variable X 6-) Let X represent the SAT score of an entering freshm
ID: 3322884 • Letter: X
Question
X. The random variable X 6-) Let X represent the SAT score of an entering freshman at University is known to have a N(1200, 90) distribution. Let Y represent the SAT score of an entering freshman at University Y. The random variable Y is known to have a N(1215, 110) distribution. A random sample of 100 freshmen is obtained from each university. Let X the sample mean of the 100 scores from University X, and Y = the sample mean of the 100 scores from University Y What is the probability that X will be 30 points greater than ?(5ptsExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2< 30
Alternative hypothesis: 1 - 2 > 30
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees offreedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 1.414
DF = 1.98
t = [ (x1 - x2) - d ] / SE
t = - 31.82
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
Therefore, the P-value in this analysis is less than 0.00001
The probability that Xbar is greater than Y bar is less than 0.0001(almost impossible).
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