Question

An organization monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 33% of students had not been absent from school even once during the previous month. In the 2000 survey, responses from 8737 randomly selected students showed that this figure had slipped to 32​%.Officials​ would, of​ course, be concerned if student attendance were declining. Do these figures give evidence of a change in student​ attendance? Complete parts a through e below.

​a) Write appropriate hypotheses.

H0​: p a)> b)< c)= d)≠ 33%

HA​: p a)> b)< c)= d)≠ 33%

​b) Check the assumptions and conditions. A) The independence assumption is plausibly justified. B)The​ 10% condition is plausibly satisfied. C)The​ success/failure condition is satisfied. ​

c) Perform the test and find the​ P-value. The test statistic is z=−1.97. ​(Round to two decimal places as​ needed.)

The​ P-value is 0.049. ​(Round to three decimal places as​ needed.) ​

d) State your conclusion. α=0.1. A) Reject the null hypothesis. B) There is sufficient evidence to conclude that the proportion of students with perfect attendance has changed.

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

A. 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. Your answer is not correct.

B. 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. This is the correct answer.

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

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

Answer 1