Find $\hat{p}$ and $\hat{q}$ . Round your answers to three decimal places.
$n = 145 and X = 81$

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Answer

Final Answer: The values of $\hat{p}$ and $\hat{q}$ are $0.559$ and $0.441$ respectively.

Steps

Step 1 ：Given that the total number of trials, n = 145 and the number of successful outcomes, X = 81.

Step 2 ：The sample proportion, $\hat{p}$ , is calculated by dividing the number of successful outcomes (X) by the total number of trials (n).

Step 3 ：So, $\hat{p}$ = $\frac{X}{n}$ = $\frac{81}{145}$ = 0.5586206896551724.

Step 4 ：The proportion of unsuccessful outcomes, $\hat{q}$ , is calculated as 1 - $\hat{p}$ .

Step 5 ：So, $\hat{q}$ = 1 - $\hat{p}$ = 1 - 0.5586206896551724 = 0.4413793103448276.

Step 6 ：Rounding these values to three decimal places, we get $\hat{p}$ = 0.559 and $\hat{q}$ = 0.441.

Step 7 ：Final Answer: The values of $\hat{p}$ and $\hat{q}$ are $0.559$ and $0.441$ respectively.