Question

The Scholastic Aptitude Test (or SAT) is a standardized college entrance test that is used by colleges and universities as a means for making admission decisions. The critical reading and mathematics components of the SAT are reported on a scale from 200 to 800. Several universities believe these scores are strong predictors of an incoming student’s potential success, and they use these scores as important inputs when making admission decisions on potential freshman. College Board President, David Coleman specified that mean test score for a student at Alex Institute of Computer Sciences is 550 or greater. The Vice President noted that the SAT scores have now been decreasing in latest years. The task is assigned to the Registrar of the Institute to monitor the sample future SAT scores to test which intuition is correct. Perform Hypothesis Testing and provide conclusion.

Answer 1

For Reading:

The hypothesis being tested is:

H0: µ 550

Ha: µ < 550

550.000	hypothesized value
598.571	mean Reading
62.029	std. dev.
23.445	std. error
7	n
6	df
2.072	t
.9582	p-value (one-tailed, lower)

Since the p-value (0.9582) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the mean test score for a student at Alex Institute of Computer Sciences is 550 or greater.

For Math:

The hypothesis being tested is:

H0: µ 550

Ha: µ < 550

550.000	hypothesized value
585.714	mean Math
82.837	std. dev.
31.309	std. error
7	n
6	df
1.141	t
.8513	p-value (one-tailed, lower)

Since the p-value (0.8513) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the mean test score for a student at Alex Institute of Computer Sciences is 550 or greater.