Question

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?

Answer #1

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

For all U.S. students nationally who take the SAT, SAT Math
scores are normally distributed with an average score of 500 for
all U.S. students and a population standard deviation of 125. A
random sample of 100 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.
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