Question

A high school principle currently encourages students to enroll in a specific SAT prep program that has a reputation of improving score by 5050 points on average. A new SAT prep program has been released and claims to be better than their current program. The principle is thinking of advertising this new program to students if there is enough evidence at the 5%5% level that their claim is true. The principle tests the following hypotheses:

H0:μ=50 points HA:μ>50 pointsH0:μ=50 points HA:μ>50 points

1. where μ is the true mean in difference of scores after the new SAT prep course is taken and before the new SAT prep course is taken. He randomly assigns 71 students to take this new SAT program. The difference in scores resulted in an average of 52.0011 points with a standard deviation of 10.9874 points.  

What is the value of the test statistic for this test? Round your answer to four decimal places.

2.A sample of 800 computer chips revealed that 42% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 39% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. State the null and alternative hypotheses.

Answer 1

1)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (52.0011 - 50)/(10.9874/sqrt(71))
t = 1.5346

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.39
Alternative Hypothesis, Ha: p ≠ 0.39