Question

A.) 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 33 arrests last month, 19 were of males aged 15 to 34 years. Use a 10% 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.)

Find the P-value of the test statistic. (Round your answer to four decimal places.)

B.)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 22 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 5% level of significance.

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

Find the P-value of the test statistic. (Round your answer to four decimal places.)

C.) The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 55 records of automobile driver fatalities in a certain county showed that 36 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use ? = 0.10.

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

Find the P-value of the test statistic. (Round your answer to four decimal places.)

D.) What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 59 college students were surveyed and r = 14 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use ? = 0.05.

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

Find the P-value of the test statistic. (Round your answer to four decimal places.)

E.) The following is based on information from The Wolf in the Southwest: The Making of an Endangered Species, by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about 50%. However, after 1918, southwestern cattle ranchers began a widespread effort to destroy wolves. In a recent sample of 37 wolves, there were only 11 females. One theory is that male wolves tend to return sooner than females to their old territories, where their predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than 50% in the region? Use ? = 0.01.

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

Find the P-value of the test statistic. (Round your answer to four decimal places.)

F.) In a fishing lodge brochure, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 62 out of a random sample of 87 guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use ? = 0.05.

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

G.) USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1009 Chevrolet owners and found that 487 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Use ? = 0.01.

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

Find the P-value of the test statistic. (Round your answer to four decimal places.)

H.) This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using the drug. It is hypothesized that regular exercise might help reduce the headaches. If a random sample of 209 patients using diltiazem exercised regularly and only 16 had headaches, would this indicate a reduction in the population proportion of patients having headaches? Use a 1% level of significance.

What is the value of the sample test statistic? (Round your answers to two decimal places.)

Find the P-value of the test statistic. (Round your answers to four decimal places.)

Answer 1

a)

p = 0.70 , P = 19/33 = 0.58 , n = 33

z = ( P - p) /sqrt(p*(1-p)/n)
= (0.58 - 0.70)/sqrt(0.70 *(1-0.70)/33)
= -1.50

p value = 0.1336

b)

p = 0.67 , P = 22/36 = 0.61, n = 36

z = ( P - p) /sqrt(p*(1-p)/n)
= ( 0.61 - 0.67)/sqrt(0.67 *(1-0.67)/36)
= -0.77

p value = 0.2206

c)

p = 0.77 , P = 36/55 = 0.65, n = 55

z = ( P - p) /sqrt(p*(1-p)/n)
= ( 0.65 - 0.77)/sqrt(0.77 *(1-0.77)/55)
= -2.11

p value = 0.0174

d)
p = 0.24 , P = 14/59 = 0.24, n = 59

z = ( P - p) /sqrt(p*(1-p)/n)
= ( 0.24 - 0.24)/sqrt(0.24 *(1-0.24)/59)
= 0

p value = 1