Question

Forty-seven percent of fish in a river are catfish. Imagine scooping out a simple random sample of 25 fish from the river and observing the sample proportion of catfish. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.

A. The standard deviation is 0.0998. The 10% Condition is met because it is very likely there are more then 250 catfish in the river.

B. The standard deviation is 0.0998. The 10% condition is not met because there are less than 250 catfish in the river.

C. The standard deviation is 0.9002. The 10% Condition is met because it is very likely there are more then 250 catfish in the river

D. The standard deviation is 0.9002. The 10% condition is not met because there are less than 250 catfish in the river

E. Unable to determine Standard deviation

Answer 1

Solution

Given that,

p = 0.47

1 - p = 1 - 0.47 = 0.53

n = 25

=  [p( 1 - p ) / n] = [(0.47 * 0.53) / 25 ] = 0.0998.

The 10% condition : Sample sizes should be no more than 10% of the population.

But a river can have more than 250 fish [where 10% of 250 =25 (sample size)

correct option is = A

The 10% condition is met because it is very likely there are more than 250 fish in the river.