Pregunta
For a large, top-rated corporation, \( 97 \% \) of employees said the corporation is a great place to work. Suppose that we will take a random sample of 7 employees. Let \( \hat{p} \) represent the proportion of employees from the sample who said the corporation is a great place to work. Consider the sampling distribution of the sample proportion \( \hat{p} \). Complete the following. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed. (a) Find \( \mu_{\hat{p}} \) (the mean of the sampling distribution of the sample proportion).
Ask by Mcfarlane Watkins. in the United States
Jan 27,2025
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(a) \( \mu_{\hat{p}} = 0.97 \)
Solución
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Bonus Knowledge
To find the mean of the sampling distribution of the sample proportion \( \hat{p} \), we use the formula: \[ \mu_{\hat{p}} = p \] where \( p \) is the true proportion of the population who think the corporation is a great place to work. Given that \( 97\% \) of employees feel this way, we convert this percentage into a decimal: \[ p = 0.97 \] Thus, the mean of the sampling distribution is: \[ \mu_{\hat{p}} = 0.97 \] In terms of formatting, when rounding to two decimal places: \[ \mu_{\hat{p}} = 0.97 \]
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