For her final project, Stacy plans on surveying a random sample of 50 students o

Question

For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for Spring Break. From past years, she guesses that about 11 % of the class goes. Is it reasonable for her to use a Normal model for the sampling distribution of the sample proportion? Why or why not? Select all that apply. A. Yes, because the data meets all the necessary conditions. B. No, because the data doesn't meet the Success/Failure Condition. C. No, because the data doesn't meet the Randomization Condition. D. No, because the date doesn't meet the Quantitative Data Condition E. No, because the data doesn't meet the 10% Condition. F. No, because the date doesn't meet the Nearly Normal Condition.

Explanation / Answer

Solution:

Given that the final project, Stacy palns on surveying a random sample of 50 students and ahe guesses that about 11% of the class goes to florida for Spring Break.
B. No, because the data doesn't meet the Success/Failure Condition
Success/Failure Condition : There are 50×11/100 = 5.5 students who go to Florida(success) and 50×89/100 = 44.5 who do not go to Florida(failures). The number of successes is less than 11. So it is not responsible to use the Normal model for the sampling distribution of sample proportion.

C. No, because the data doesn't meet the Randomization Condition
Randomization Condition: The sample is a random sample. So the respondents should be independent.

E. No, because the data doesn't meet the 10% Condition
10% condition : The population of students is very large(more than 500). So the 10% condition is satisfied.

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