Question

It is claimed that 68% of college students change their majors at least once. A researcher believes this claimed value is too low. He surveys a random sample of 247 college students and finds that 72% of them have changed their majors at least one time. Use this information to conduct a hypothesis test at a significance (or alpha) level of 0.05.

What will the hypotheses be?

H_o:

H_a:

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.68

H_a : p < 0.68

n =247

=0.72

P₀ = 0.68

1 - P₀ = 1 - 0.68 =0.32

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.72-0.68/ [(0.68*0.32) / 247 ]

= 1.35

Test statistic = z = 1.35

P(z < 1.35) = 0.9115

P-value = 0.9115

= 0.05

P-value >

0.9115 > 0.05

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that