Question

In a certain large state university, older students get to choose their classes before younger students; that often means that freshmen don't get to take the classes they want. Jacob wants to take a really popular course in Russian literature, but his adviser says there's only a 30% chance that it will be available when he gets to choose his classes. Jacob wonders if his chances are actually better than 30% since in the past few years, 73 of 200 freshmen who requested the course were able to get in. Do these data provide good evidence that freshmen have a better than 30% chance of getting the course if they ask for it?

(a)

What is the null hypothesis?

H₀: p = 0.30H₀: p < 0.30    H₀: p > 0.30H₀: p ≠ 0.30

(b)

What is the alternative hypothesis?

H_a: p = 0.30H_a: p < 0.30    H_a: p > 0.30H_a: p ≠ 0.30

(c)

What is the value of p̂?

p̂ =

(d)

What is the value of z? (Round your answer to two decimal places.)

z =

(e)

What is the P-value for this test? (Use a table or technology. Round your answer to four decimal places.)

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.30

H_a : p > 0.30

$\hat p$ = x / n = 73 / 200 = 0.365

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.365 - 0.30 / [$\sqrt$(0.30 * 0.70) / 200]

z = 2.01

P-value = 0.0224