Question

An organization monitors many aspects of elementary and secondary education nationwide. Their 1995 numbers are often used as a baseline to assess changes. In 1995, 33% of students had not been absent from school even once during the previous school year. In the 1999 survey, responses from 8217 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. Ho: HA: b) Check the assumptions and conditions. The independence assumption justified. The 10% condition satisfied. The success/failure condition satisfied. c) Perform the test and find the P-value. The test statistic is z= (Round to two decimal places as needed.) The P-value is O (Round to three decimal places as needed.) d) State your conclusion. Use a = 0.1. the null hypothesis. There sufficient evidence to conclude that the proportion of students with perfect attendance

Answer 1

Given ,

Po = 33% 0.33

$n=8217$

$\hat{p}=32\%=0.32$

a] given claim : proportion changes from 33%

The claim is either the null or alternative hypothesis , the null hypothesis states that the population proportion is equal to the value mentioned in claim , that is we write hypothesis as

$H_0:p=0.33$

$H_a:p \neq 0.33$

b] the independence assumption is justified

The 10% condition is satisfied because 8302 students is less than 10% of all students

The success/ failure condition is satisfied since $np_0$ and  $n(1-p_0)$ are both atleast 10.

c] the value of test statistic is

$z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}=\frac{0.32-0.33}{\sqrt{\frac{0.33(1-0.33)}{8217}}}=\boldsymbol{-1.93}$

we get p value as 0.054

d] at significance level 0.1 , we get that 0.1 > p value , that is

reject the null hypothesis , There is sufficient evidence to concude that the proportion of students with perfect attendance changes