Question

1. In many animal societies, a role assumed by the adult male is a sentry, warning adult females and juveniles of approaching predators. Some students of animal behavior believe that this occurs in human society also. In one 4-month study in Seattle an investigator observed people crossing the street at an intersection with no traffic control. The observed behavior was the scanning behavior ("looking both ways") of adult males and females. The investigator reasoned that if the adult male assumed a protective sentry role, the scanning rate when alone would be less than when accompanied by an adult female. Data from this study is given below. Conduct hypothesis test using a=.05. Please show all work. If you use computer software (minitab, program R or excel) please show the computer output.

Male Scanning ("Looking both ways") Behavior Situation            Scanned       Did Not             Totals Scan
Alone	56	28	84
With adult female	61	15	76

Ho:

Ha:

Rejection region

value of test statistic

p-value

state your conclusion

Answer 1

Consider two populations.

1^st population consists of those male who scanned when alone.

2^nd population consists of those male who scanned when with adult female.

Let P₁ and P₂ denote the first and second population proportion(scanning rate) respectively.

If the adult male assumed a protective sentry role, the scanning rate when alone would be less than when accompanied by an adult female.

So we have to test P₁ < P₂. So the null and alternative hypothesis are

Here significance level, = 0.05

The rejection region is  

First sample size, n₁ = 84

Second sample size, n₂ = 76

First sample proportion, P₁' = 56/84

Second sample proportion, P2' = 61/76

p = (56+61)/(84+76) = 117/160

q = 1-p = 43/160

The test statistic is

Value of test statistic, z = -1.937

p-value = 0.026

• Since z=-1.937 is less than -1.645, we reject the null hypothesis.
• p-value approach : Since p-value < , we reject the null hypothesis.

We reject the null hypothesis.

Scanning rate when alone is less than when accompanied by an adult female.

The conclusion is: The adult male assumed a protective sentry role.

------------------------------------------------------------------------------------------------------------------------------------------------------------