Question

Suppose the true proportion of voters in the county who support a new fire district is...

Suppose the true proportion of voters in the county who support a new fire district is 0.58. Consider the sampling distribution for the proportion of supporters with sample size n = 138. What is the mean of this distribution? (Enter your answer accurate to two decimal places.) What is the standard deviation of the sampling distribution (i.e. the standard error)? (Enter your answer accurate to three decimal places.)

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Answer #1

Solution :

a) The mean of the sampling distribution of proportion is equal to true value of population proportion.

i.e.  

We have, true value of proportion of voters in the county who support a new fire district (p) = 0.58

Hence, the mean of the sampling distribution of proportion is 0.58.

b) The standard deviation of the sampling distribution of proportion is given as follows :

Where, p is true value of proportion and n is sample size.

We have, p = 0.58 and n = 138

Hence, standard deviation of the sampling distribution is,

The standard deviation of the sampling distribution is 0.042.

Please rate the answer. Thank you.

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