For all U.S. students nationally who take the SAT, the average SAT Math score is 500, with a population standard deviation of 125. A random sample of 10 students entering Whitmer College had an average SAT Math (SAT-M) score of 530. The sample data can be used to test the claim that the mean SAT-M score of all Whitmer College students is different than the national mean SAT-M score. Based on the given information, have the conditions for this hypothesis test been satisfied?
Solution :
=
530
=500
=125
n = 10
This is the two tailed test .
The null and alternative hypothesis is ,
H0 : =
530
Ha :
530
Test statistic = z
= (
-
) /
/
n
= (500-530) / 125 /
10
= -0.76
Test statistic = z = -0.76
P(z < -0.76 ) = 0.2236
P-value = 2 * 0.2236 =0.4472
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