Answer to Question #131429 in Statistics and Probability for Keagan

Question

1.1.A college professor randomly selects 25 freshmen to study the mathematical background of the
incoming freshman class. The average SAT score of these 25 students is 565 and the standard deviation
is estimated to be 40. Using this information, can the professor reject the null hypothesis that the
average test score is 550 or less?
Use a 5 % level of significance.
1.2.Suppose the college professor in question 1.1. wants to know whether the mathematical aptitude
of freshmen has improved over the past year. He randomly draws 25 SAT mathematics scores from
last year’s freshman class and obtains a sample mean of 560 and a sample standard deviation of 35.
Compare the results from last year with the results from this year. Do the data offer enough evidence
for rejecting the null hypothesis that there is no improvement?
Use a 5 % level of significance.

Answer 1

QUESTION1.1

Ho : u≤ 550 vs H1> 550

mean(µ) = 550,x= 565, square root(∂) = 40 and n =25 ,significance level(0.05)

z =(x-µ)/(40/√n)

z= (565-550)/(40/5)

z= 1.875

p-value =0.0301 since the p-value is less than significance level reject the null hypothesis

QUESTION1.2

Ho : u ≤ 550 vs H1> 550

mean(µ) = 550,x > 560, square root(∂) = 35 and n =25 ,significance level(0.05)

z =(x-µ)/(∂/√n)

z= (560-550)/(35/5)

z= 1.43

p-value =0.0764 since the p-value is greater than significance level fail reject the null hypothesis and conclude average test score is 550 or less.