A recent 0ypotheticaj study of 4,000 first graders found that 23% were able to r

Question

A recent 0ypotheticaj study of 4,000 first graders found that 23% were able to recite alphabet before they entered the first grade. An older study of 2500 first graders from the 1970s found that 17% of students were able to recite the alphabet before they entered the first grade. Use a test of significance to determine if there is a difference between first graders in the 1970s and first graders today when it comes to reciting the alphabet. Below; state your hypotheses, state your conclusion and what was the observed significance level. Submit your work leading up to this conclusion by E-mail YOU MUST SUBMIT YOUR WORK FOR THIS PROBLEM T T | (Paragraph : | Arial :113 (12pt) :) :-·-·T , Path: p Words:0

Explanation / Answer

Given that,
sample one, x1 =920, n1 =4000, p1= x1/n1=0.23
sample two, x2 =425, n2 =2500, p2= x2/n2=0.17
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.025
from standard normal table, two tailed z /2 =2.241
since our test is two-tailed
reject Ho, if zo < -2.241 OR if zo > 2.241
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.23-0.17)/sqrt((0.207*0.793(1/4000+1/2500))
zo =5.809
| zo | =5.809
critical value
the value of |z | at los 0.025% is 2.241
we got |zo| =5.809 & | z | =2.241
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 5.8094 ) = 0
hence value of p0.025 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: 5.809
critical value: -2.241 , 2.241
decision: reject Ho
p-value: 0

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