Question

Dan believes the success rate of students who take a morning class is higher than students who take an afternoon class in the same subject. In a morning class of 34 students, 30 have passing grades (C or better). In an afternoon class of 25 students, 18 have passing grades.

What is H₀:

What is Ha:

What is the p-value? Round answer to three decimal places (i.e. 0.123)? Answer

At a level of significance (alpha) of 0.05, what is your decision?

reject the null hypothesis

accept the null hypothesis

fail to reject the null hypothesis

Answer 1

Solution :

Given that,

n₁ = 34

x₁ = 30

Point estimate = sample proportion = ₁ = x₁ / n₁ = 0.88

n₂ = 25

x₂ = 18

Point estimate = sample proportion = ₂ = x₂ / n₂ = 0.81

The value of the pooled proportion is computed as,

= ( x₁ + x₂ ) / ( n₁ + n₂ )

= (30 + 18 ) / ( 34 + 25)

= 0.81

1 - = 0.19

Level of significance = = 0.05

This a right(one)-tailed test.

The null and alternative hypothesis is,

Ho: p₁ = p₂

Ha: p₁ > p₂

Test statistics

z = (₁ - ₂ ) / *(1-) ( 1/n₁ + 1/n₂ )

= (0.88 - 0.72 ) / (0.81 * 0.19 ) (1/34 + 1/25 )

= 1.582

P-value = P(Z > z )

= 1 - P(Z< 1.582)

= 1 - 0.9432

= 0.057

Since, P-value = 0.057 > 0.05 , It is concluded that fail to reject null hypothesis.

fail to reject the null hypothesis