Question

A private lake sells boating memberships and currently has 600 members. During the application process the potential members are asked which recreational activity they do the most. Their choices are fishing, skiing, boarding, swimming, or tubing. The lake manager chooses clients according to their interests to maximize the use of all areas of the lake. Every month, the lake rangers randomly sample the boats on the lake and categorize them according to the activity they are doing. The lake manager performs a chi-square goodness-of-fit test using the following null hypothesis to see whether their samples differ significantly from what the original applications claim.

H0:pfish=0.26,pski=0.21,pboard=0.30,pswim=0.12,ptube=0.11
In order to meet the conditions for independence and large counts for a chi-square goodness-of-fit test, which of the following represents all possible sizes of the monthly samples?
a. n≥30
b. 30≤n≤50
c. 46≤n≤60
d. n≥46
e. n≤60

Answer 1

46 ≤ n ≤ 60 ( C )

Explanation:

using the given null hypothesis to check if the samples differ from originally values

given that: frequency ( f ) ≥ 5

N = 600

hence : n * 0.11 ≥ 5

therefore : n ≥ 45.45

next : also n / N ≤ 0. 10

therefore: n ≤ 0.1 * 600

therefore all possible sizes will lie between

46≤n≤60