A recent survey asked 1000 people of different ages to express their preference between traditional shopping and online shopping. The resulting data are presented below.

Given this data, what is the (empirical) probability that a particular respondent is Gen X given they are an online shopper?

Note: Round probabilities to 2 decimal places.

Question

A recent survey asked 1000 people of different ages to express their preference between traditional shopping and online shopping. The resulting data are presented below.

Given this data, what is the (empirical) probability that a particular respondent is Gen X given they are an online shopper?

Note:  Round probabilities to 2 decimal places.

BlackTom AI · Accepted Answer

The question asks for the empirical probability that a respondent is Gen X given that they are an online shopper, i.e., P(Gen X | Online). This is computed as the number of Gen X online shoppers divided by the total number of online shoppers.

Option-by-option analysis:
- Option 0.17: If this were the computed ratio, it would mean Gen X online shoppers are 17% of all online shoppers. To assess its validity, we would need the actual counts: Gen X among online shoppers divided by total online shoppers. Without the data, we cannot confirm this value.
- Option 0.34: This would indicate 34% of online shoppers are Gen X. Again, the determination depends on the specific tallies of Gen X online vs. all online shoppers; the same data requirement applies.
- Option 0.50: A 50% probability would imply Gen X constitutes half of online shoppers. This is only plausible if the counts show Gen X online equals the total online shopper count, which needs verification from the data.
- Option 0.67: A 67% share suggests Gen X online shoppers are two-thirds of all online shoppers. This requires the corresponding counts to be checked against the online shopper total.
- Option 0.84: An 84% probability would mean a large majority of online shoppers are Gen X, again contingent on the actual data tallies.
- None of the answers are correct.: This option is selected if none of the numerical percentages match the computed ratio from the given data.

Key observation: The dataset or counts needed to compute P(Gen X | Online) are not visible in the prompt presented here (the image likely contains the contingency data). To determine which option is correct, you would extract the number of Gen X respondents who are online and the total number of online respondents from the survey, then compute (Gen X online) / (Total online), rounding to two decimals as required. Then compare the result to the listed options. Any conclusion about which option is correct would require those actual counts.

If you provide the explicit contingency table or the raw counts (Gen X online, Gen X total online, etc.), I can carry out the exact calculation and identify the correct option, showing the arithmetic and rounding steps. Until then, each of the numerical options could be correct or incorrect depending on the data, so labeling a specific numeric choice would be speculative without the data.

MGMT 101 LEC ONL: MANA... Study Checkpoint 9: Decision Analysis II

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