Question

the national center for education statistics monitors many aspects of elementary and secondary education nationwide. their 1996 numbers are often used as a baseline to assess changes. in 1996, 34% of students had not been absent from school even once during the previous school year. in a 2000 survey, responses from 8705 students showed that this figure had slipped to 33%. 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.

h₀: p = 34%
hₐ: p ≠ 34%

b) check the assumptions and conditions.
the independence assumption is plausibly justified.
the randomization condition is plausibly satisfied.
the 10% condition is plausibly satisfied.
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 (round to three decimal places as needed.)

Explanation:

Step1: Identify test type

This is a two-tailed z-test for a population proportion.

Step2: Find single-tail area

For $z=-1.97$, the area to the left of $z$ is $P(Z < -1.97) = 0.0244$.

Step3: Calculate two-tailed P-value

Double the single-tail area for the two-sided alternative hypothesis.
$P\text{-value} = 2 \times 0.0244$

Answer:

0.049