Question at position 19 The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours. The CEO selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the point estimate of the proportion of the population that logged onto Facebook that day? NOTE: Please provide your calculation and final answer in separate blank spaces. Calculation is : Question Blank 1 of 2[input], Final answer is: Question Blank 2 of 2[input].

Question

BlackTom AI · Accepted Answer

First, restating the scenario: a random sample of n = 150 employees is taken, and x = 53 of them used Facebook during work hours. The goal is to estimate the population proportion p by the point estimate p-hat.

Step 1: Compute the point estimate. The standard estimator for a proportion is p-hat = x / n. Substituting the observed values gives p-hat = 53 / 150.

Step 2: Perform the division. 53 divided by 150 equals 0.353... (repeating 3s after the decimal).

Step 3: Interpret and report the result. The point estimate of the population proportion who logged onto Facebook is approximately 0.353 when rounded to three decimal places. If someone rounds differently, you might see 0.3533... or 0.353 as a conventional reporting choice.

Addressing potential alternative representations:
- If you were to report as a percentage, you would multiply by 100 to get about 35.3%. 
- If you round to two decimals, you would get 0.35 (or 35%).

Applied to the provided blank structure:
- Calculation is : 53/150
- Final answer is: 0.353

Notes on common mistakes:
- Using 150/53 would invert the proportion and give a meaningless value in this context.
- Rounding to fewer decimals changes precision but not the underlying estimate; 0.353 is a precise three-decimal representation of 53/150.
- If someone mistakenly uses a sample proportion from a different sample size, the estimate would be inconsistent with the observed data.

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