Answer :
To meet the conditions of independence and large numbers for the chi-square good-of-fit test, then the representative of all possible monthly sample sizes is n ≤ 60.
To meet the conditions of independence and large numbers for the chi-square good-of-fit test, then the representative of all possible monthly sample sizes is n ≤ 60.
The chi-square fit test is appropriate when the following conditions are met: The sampling method is simple random sampling. The variables studied are categorical. The expected value of the number of observation samples at each variable level is at least 5.
In question:
Since the expected frequency for each category should be at least 5.
therefore n*0.11 ≥ 5
n ≥ 46
also, n/N ≤ 45/5 = 0.10
The boating group has 600 members:
n ≤0.1*600
n ≤ 60
So, the possible monthly sample size is n ≤ 60.
Your question is incomplete but most probably your full question was:
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: p-[tex]_{fishing}[/tex]=0.26, p-[tex]_{skiing}[/tex] =0.21, p-[tex]_{boarding}[/tex]=0.30, p-[tex]_{swimming}[/tex]=0.12, p-[tex]_{tubeing}[/tex]=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
The correct answer is C.
Learn more about the chi-square goodness-of-fit test at https://brainly.com/question/17228811.
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