Question

1)      Historically, at a particular university, 75% of incoming freshman scored at the “college ready” level in math. The admissions office believes that more students today are scoring at the “college ready” level. A sample of 78 incoming freshmen found that 64 are scoring at the “college ready” level. Is there enough evidence to support the admission’s office claim at the a=0.01 level?

a.       State the null and alternative hypotheses using proper notation.

b.       Use StatCrunch to calculate the test statistic and P-value.

c.       At a = 0.05, do you reject the null hypothesis? YES / NO

d.       There (circle one: is   /   is not ) evidence to suggest that today more freshmen at this university (circle one: are / are not) scoring at the college-ready level.

2)      Using the data from problem 1, calculate a 99% confidence interval.

a.       Use StatCrunch to calculate the confidence interval. Write your answer in a form similar to (15.44%, 18.36%).

b.       Write a sentence summarizing your findings in the context of the problem.

Answer 1

Ans:

1)a)

b)sample proportion=64/78=0.8205

Test statistic:

z=(0.8205-0.75)/sqrt(0.75*(1-0.75)/78)

z=1.438

p-value=P(z>1.438)=0.0752

c)As,p-value>0.05,we do not reject the null hypothesis.

No

d)There is not evidence to suggest that today more than 75% freshmen at this university are scoring at the college-ready level.

2)

a)99% confidence interval for p

=0.8205+/-2.576*sqrt(0.8205*(1-0.8205)/78)

=0.8205+/-0.1119

=(0.7086, 0.9324)

or (70.86%, 93.24%)

b)As,above CI include 75% within its limits,there  is not evidence to suggest that today more than 75% freshmen at this university are scoring at the college-ready level.