Asked by Nicole Salazar on Jul 02, 2024

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Which of the following best describes the form of the sampling distribution of the sample proportion?

A) When standardized, it is exactly the standard normal distribution.
B) When standardized, it is the t distribution.
C) It is approximately normal as long as n Which of the following best describes the form of the sampling distribution of the sample proportion? A)  When standardized, it is exactly the standard normal distribution. B)  When standardized, it is the t distribution. C)  It is approximately normal as long as n   30. D)  It is approximately normal as long as np   5 and n(1 - p)    5. 30.
D) It is approximately normal as long as np Which of the following best describes the form of the sampling distribution of the sample proportion? A)  When standardized, it is exactly the standard normal distribution. B)  When standardized, it is the t distribution. C)  It is approximately normal as long as n   30. D)  It is approximately normal as long as np   5 and n(1 - p)    5. 5 and n(1 - p) Which of the following best describes the form of the sampling distribution of the sample proportion? A)  When standardized, it is exactly the standard normal distribution. B)  When standardized, it is the t distribution. C)  It is approximately normal as long as n   30. D)  It is approximately normal as long as np   5 and n(1 - p)    5. 5.

Sampling Distribution

A distribution indicating the probabilities of a statistic, which is calculated from a random sample.

Sample Proportion

The fraction of the sample that represents a particular attribute or characteristic.

  • Compute likelihoods for binomial distributions and comprehend the distributions of sample data.
  • Understand the application of the Central Limit Theorem in approximating sampling distributions.
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Mariah BrighamJul 02, 2024
Final Answer :
D
Explanation :
The sampling distribution of the sample proportion is approximately normal when the sample size is large enough, but since we don't know the population standard deviation, we cannot use the standard normal distribution for it. Moreover, since we are dealing with proportions, the t distribution is not appropriate either. Therefore, the only valid option is to use the approximate normality condition based on the sample size and the sample proportion, which is given by np ≥ 5 and n(1-p) ≥ 5. Option D correctly captures this condition.