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

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