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The administrator responsible for reserving and preparing rooms for the final examination needs an estimate of the number of left-handed students out of the total number of students taking MATH381 to provide the optimal number of left-handed armchairs. In a random sample of [tex]n=50[/tex] students, it is found that 34 of them are left-handed. Which statement is true about the estimator [tex]p[/tex] of the actual proportion of left-handed students, when [tex]p[/tex] is the ratio of the success number to the size of the sample?

A. It is approximately normally distributed.
B. It is random with a standard deviation of [tex]\sqrt{\frac{p(1-p)}{n}}[/tex].
C. All of the other statements are true for this sample.
D. [tex]p=\frac{34}{50}[/tex]

Answer :

Final answer:

The correct statement about the estimator p is that it is approximately normally distributed and its standard deviation is given by sqrt(p(1-p)/n).

Explanation:

The question is asking about the properties of the estimator p, which represents the proportion of left-handed students in the population based on the sample. In this case, the sample size is n=50 and the number of left-handed students is 34.

The estimator p is approximately normally distributed when certain conditions are met. This means that if we were to take multiple random samples of the same size, the distribution of the sample proportions would be approximately normal.

The standard deviation of the estimator p is given by sqrt(p(1-p)/n). This formula takes into account the variability in the sample proportions and decreases as the sample size increases.

Therefore, the correct statement about the estimator p is that it is approximately normally distributed and its standard deviation is given by sqrt(p(1-p)/n).

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