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? H: P = 0.30 HO:p <0.30 Ho:p> 0.30 Hop +0.30 (b) What is the alternative hypothesis? OH: P = 0.30 H: p < 0.30 II VA Hy: p > 0.30 HP 0.30 (c) What is the value of p? p = (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

The statistic software output for this problem is:

One sample proportion summary hypothesis test: P: Proportion of successes Ho: P = 0.3 HA: p > 0.3 Hypothesis test results: Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value 73 200 0.365 0.032403703 2.0059435 0.0224

(a) Null : H₀ : p = 0.3

(b) Alternative :  H_A : p > 0.3

(c) p-hat = 0.365

(d) z = 2.01

(e) P-value = 0.0224