Question

An organization monitors many aspects of elementary and secondary education nationwide. Their 2000 numbers are often used as a baseline to assess changes. In 2000, 31% of students had not been absent from school even once during the previous month. In the 2004 ​survey, responses from 8440 randomly selected students showed that this figure had slipped to 30%. Officials​ would, of​ course, be concerned if student attendance were declining. Do these figures give evidence of a change in student​ attendance?

A) Perform the test and find the​ P-value.

B) State your conclusion. Fill in the blank below.

(Reject/Fail to Reject) the null hypothesis. There (is/is not) sufficient evidence to conclude that the proportion of students with perfect attendance (has changed/has not changed/has increased/has decreased).

C) Do you think this difference is​ meaningful? Explain.

A. The difference is probably not meaningful. The observed change in the sample is quite​ small, so even though it is statistically​ significant, it does not indicate a large enough change to be meaningful.

B. The difference is not meaningful because it is not statistically significant.

C. The difference is probably meaningful because the observed change in the sample is large enough to be important and the results indicate that it is statistically significant.

D. The difference must be meaningful because it is statistically significant.

Answer 1

Ans:

a)

Test statistic:

z=(0.3-0.31)/SQRT(0.31*(1-0.31)/8440)

z=-1.986

p-value(2 tailed)=2*P(z<-1.986)=2*0.0235=0.0470

b)As,p-value<0.05

Reject the null hypothesis. There is sufficient evidence to conclude that the proportion of students with perfect attendance has changed.

c)Option A is correct.

The difference is probably not meaningful. The observed change in the sample is quite​ small, so even though it is statistically​significant, it does not indicate a large enough change to be meaningful.

*(it is statistically significant,as sample size is very large)