In 2000, a study of HCC algebra students says that 65% of them pass on their first attempt. In 2004, a survey of 450 algebra students reported that 287 passed on their first attempt. Is there sufficient evidence to suggest that the number of students that passed in 2004 is different than in 2000

Answer:The calculated value Z = 0.549 < 1.96 at 0.05 level of significanceNull hypothesis is accepted There is no difference between the number of students that passed in 2004 and 2000Step-by-step explanation:Step(i):-Given Population proportion 'P' = 65% or 0.65Given 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   2000Alternative Hypothesis :H₁: The number of students that passed in 2004 is different than in 2000Step(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| = 0.549The critical value z₀.₀₅ = 1.96The calculated value Z = 0.549 < 1.96 at 0.05 level of significanceFinal answer:-Null hypothesis is accepted There is no difference between the number of students that passed in 2004 and 2000