Question

2) Suppose that scores on the SAT form a normal distribution with μ = 500 and σ = 100. A high school counselor has developed a special course designed to boost SAT scores. A random sample of n = 16 students is selected to take the course and then the SAT. The sample had an average score of 554. Does the course have an effect on SAT scores?

    a) What are the dependent and independent variables in this experiment?

    b) Perform the hypothesis test using α = .05.

    c) If α = .01 were used instead, what z-score values would be associated with the critical region?

    d) For part c), what decision should be made regarding H₀? Compare to part b), and explain the

         difference.

Answer 1

Answer 2a)

The dependent variable is SAT score

The independent variable is Taking special course

Answer 2b)

Thus, at 0.05 significance level, there is enough evidence to support the claim that course have an effect on SAT scores.

Answer 2c)

Critical z value corresponding to α=0.01 for a right tailed test is zc ​= 2.33 (Obtained using critical z value calculator)

Answer 2d)

Since it is observed that z = 2.16 ≤ zc​ = 2.33, we fail to reject null hypothesis.

Therefore, there is not enough evidence to claim that the population mean μ is greater than 500, at the 0.01 significance level. In other words, at 0.01 significance level, there is not enough evidence to support the claim that course have an effect on SAT scores.