Respuesta :
Answer:
The calculated value Z = 0.549 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
There is no difference between the number of students that passed in 2004 and 2000
Step-by-step explanation:
Step(i):-
Given Population proportion 'P' = 65% or 0.65
Given survey of 450 algebra students reported that 287 passed on their first attempt.
Sample proportion
[tex]p = \frac{x}{n} = \frac{287}{450} = 0.6377[/tex]
Null Hypothesis :H₀: The number of students that passed in 2004 is equal to 2000
Alternative Hypothesis :H₁: The number of students that passed in 2004 is different than in 2000
Step(ii):-
Test statistic
[tex]Z = \frac{p - P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.6377 - 0.65}{\sqrt{\frac{0.65 x 0.35}{450} } }[/tex]
[tex]Z = \frac{-0.0123}{0.0224} = -0.549[/tex]
|Z| = |-0.549| = 0.549
The critical value
z₀.₀₅ = 1.96
The calculated value Z = 0.549 < 1.96 at 0.05 level of significance
Final answer:-
Null hypothesis is accepted
There is no difference between the number of students that passed in 2004 and 2000
