Question
What is the value of \( \hat{p} \) when \( x=120 \) and \( n=100 ? \)
Ask by Curry Pope. in the Philippines
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \hat{p} = 1.2 \)
Solution
1. The formula for the sample proportion is given by
\[
\hat{p} = \frac{x}{n}.
\]
2. Substitute \( x = 120 \) and \( n = 100 \) into the formula:
\[
\hat{p} = \frac{120}{100}.
\]
3. Simplify the fraction:
\[
\hat{p} = 1.2.
\]
Thus, the value of \( \hat{p} \) is \( 1.2 \).
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Simplify this solution The Deep Dive
To find the value of \( \hat{p} \), which represents the sample proportion, you can use the formula: \[ \hat{p} = \frac{x}{n} \] In your case, \( x = 120 \) and \( n = 100 \). Simply plug in the values: \[ \hat{p} = \frac{120}{100} = 1.2 \] However, since a proportion cannot exceed 1, it seems there may be a misunderstanding in the values provided. Please double-check if \( x \) (the number of successes) should indeed be less than or equal to \( n \) (the total trials).
