Question

A study considers how the college entrace exam scores for students in 2018

compared to that of the students in 1988. The national mean score in 1988 in 500 (out of

1000 possible points). Based on a simple random sample of 10,000 students, the 2018

sample mean socre is 497 (out of 1000 possible points), and the standard deviation s=100.

1.1 State the null and the alternative hypotheses, and explain your reasoning for choosing an one-sided or a two-sided test.

2.2 Compute the test statistic. Show your work.

2.3 A statistical software finds that the corresponding p-value equals 0.008. At α= 0.01, interpret the result.

2.4 Is the result practically significant? Why or why not?  

2.5 Increasing from 0.001 to 0.01, how does the probability of Type I error change? How does the probability of Type II error change?

Answer 1

Solution1.1:

Ho:

Ha:

two sided test as nothing increase or decrease specified in claim.Its only stating

The national mean score in 1988 in 500 (out of

1000 possible points)

2.2 Compute the test statistic. Show your work.

t=xbar-mu/s/sqrt(n)

=(497 -500)/(100/sqrt(10000 ))

t=-3

2.3 A statistical software finds that the corresponding p-value equals 0.008. At α= 0.01, interpret the result.

p=0.008

alpha=0.01

p<alpha

Reject Ho

There is no sufficient statistical evdience at 5% level of significance to conlcude that

mean score for  college entrace exam scores for students in 2018

is same as that of the students in 1988.

That is mean score for  college entrace exam scores for students has changed from the national mean score in 1988

2.4 Is the result practically significant? Why or why not?  

Result is practically significant as p<0.01