Question

64% of students will apply for graduate school. from a sample of 100 students, 52 stating that they will apply for grad school. for alpha=.01 you ___ hypothesis

Answer 1

Answer:

you accept the alternative hypothesis

Step-by-step explanation:

The null and alternative hypothesis can be computed as follows:

$H_o: p = 0.64 \\ \\ H_1: p \le 0.64$

The sample proportion $\hat p = \dfrac{x}{n}$

$\hat p = \dfrac{52}{100}$

$\hat p = 0.52$

The test statistics can be computed as:

$Z = \dfrac{\hat p -p_o}{ \sqrt{ \dfrac{p_o \times (1-p_o)}{ n} }}}$

$Z = \dfrac{0.52 -0.64}{ \sqrt{ \dfrac{0.64 \times (1-0.64)}{ 100} }}}$

Z = -2.5

The P-value = 2( Z< -2.5)

From the tables;

The P-value = 2 (0.0062)

The P-value = 0.0124

The significance level = 0.01

Since the P-value is > significance level; we fail to reject the null hypothesis.

Conclusion: we accept the alternative hypothesis