Question

3. At CSUF, a simple random sample of 100 entering graduate students in 2018 found that 20 of the sampled students in the bottom third of their undergraduate class. Admission standards were tightened in 2019. In 2019, a simple random sample of 100 entering graduate students found that only 10 finished bottom third of their undergraduate class. Let P, and p, be the proportions of all entering graduate students in 2018 and 2019, respectively, who graduated in the bottom third of their undergrad class. Is there evidence that the proportion of graduate students who graduated in the bottom third of their undergrad classes in 2019 was reduced as a result of the tougher admission standards adopted in 2018, compared to the proportion in 2018? List all 4 steps of performing a test of significance. [12 points)

Answer 1

Sample 1: Sample number of events Sample size 20 Given 100 Given Sample proportion Pi= 41= 0.2 Sample 2: Sample number of events 10 Given Sample size 100 Given Sample proportion Þ2 = *2 = 0.1 Pooled proportion MP1+12P2 = 0.15 ni +n2 Ho: P1 = P2 H:P,> P2 Null hypothesis Alternative hypothesis Level of significance a = 0.05 say Right tailed Critical value = 1.65 From z table Rejection region :z> 1.65 Standard error Point estimate à - 72 = 0.1 Test statistic: Part 13 p-value: For z= 1.98 the right tailed p-value is 0.02385 Decision: Reject Ho because p-value <a Conclusion : There is enough evidence