Question

Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 36 women athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 10% level of significance

What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 38 arrests last month, 23 were of males aged 15 to 34 years. Use a 5% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%

What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.67
Alternative Hypothesis, Ha: p < 0.67

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.5833 - 0.67)/sqrt(0.67*(1-0.67)/36)
z = -1.11

P-value Approach
P-value = 0.1335

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.7
Alternative Hypothesis, Ha: p ≠ 0.7

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.6053 - 0.7)/sqrt(0.7*(1-0.7)/38)
z = -1.27

P-value Approach
P-value = 0.2041