Which of the following scenarios would it be appropriate to use normal approxima

Question

Which of the following scenarios would it be appropriate to use normal approximation for the sampling distribution of the proportion?

Select all that apply.

Select one or more:

A researcher wishes to find the probability that less than 5% of a sample of undergraduate students from Appalachian State University will be between the ages of 25 and 34. He randomly samples 60 undergraduate students from the student database. The population proportion of undergraduates between the ages of 25 and 34 is 5.3%.

A grad student at NC State wants to know how likely it is that a group of students would be made up of more than 27% graduate students. She will randomly select 38 students and ask them if they are a graduate student or an undergraduate student. The population proportion of grad students at NC State is 26.6%

A full time student at Fayetteville State University wants to know how likely it is that a group of students would be made up of less than 70% full time students. She will ask 20 people that she sees parking in the parking deck if they are full time or part time. The population proportion of full time students at Fayetteville State is known to be 72%

first one is wrong please give exact procedure

Explanation / Answer

The assumptions for normal approximation for sampling distribution of proportion are as follows:

1. Samples should be drawn at random, so that the samples become true representative of the population.

2. Both number of events, x and number of trials-number of events, that is n-x should be atleast 5.

Consider scenario 1. The reseracher used convinience sampling (where, researcher sampled the first 42 students who arrived in the gym at Monday morning) and therefore, the sampling scheme is biased (sample is not representative of the population-undergraduate students from UNC). The first condition being not fulfilled, normal approximation for sampling distribution of proportion cannot be applied.

Scenario 2. Here, randomization condition is fulfilled (researcher randomly sampled 60 undergraduate students from data base). The second condition, that is both n=60, and n-x=60-(60*0.05)=57 are far off from 5. Therefore, normal approximation for sampling distribution of proportion cannot be applied.

Scenario 3. Here, randomization condition is fulfilled (researcher randomly sampled 38students). The second condition, that is both n=38, and n-x=38-(38*0.27)=28 are far off from 5. Therefore, normal approximation for sampling distribution of proportion cannot be applied.

cenario 4. The reseracher used convinience sampling (where, researcher sampled 20 people that she came across in the parking deck) and therefore, the sampling scheme is biased (sample is not representative of the population-full time students at Fayetteville State University). The first condition being not fulfilled, normal approximation for sampling distribution of proportion cannot be applied.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.