MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
A sample of size 31 was gathered from high school seniors to estimate how many intended to attend the state university. It is known that the proportion of the population answering "yes" was 0.7. What are the mean and standard deviation, and standard error of the mean of this sample? \[ \text{mean} = E\left(\hat{p}\right) = \text{[textbox]} \] \[ \text{standard error} = SD\left(\hat{p}\right) \text{ (accurate to 3 decimal places) } = \text{[textbox]} \]
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Transcribed Image Text:A sample of size 31 was gathered from high school seniors to estimate how many intended to attend the state university. It is known that the proportion of the population answering "yes" was 0.7. What are the mean and standard deviation, and standard error of the mean of this sample? \[ \text{mean} = E\left(\hat{p}\right) = \text{[textbox]} \] \[ \text{standard error} = SD\left(\hat{p}\right) \text{ (accurate to 3 decimal places) } = \text{[textbox]} \]
Expert Solution
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The proportion of a group or sample is calculated as the number of successes divided by the total number of trials. In case of a population of size N, if x is the number of successes then the population proportion is given by p=xN. Similarly, in the case of a sample of size n, the sample proportion is given by p^=xn.

 

Here, the number of successes x follows the binomial distribution with probability p and number of trials n.

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