Waulmodic 2 \( C D=24= \) The manager of a gym selected a sample of 139 members at random to estimate tre percentage of the grry members that would continue to pay for a membership if the price increased. From the surve, fte marager estimates tiat \( 32 \% \) of the gym's members would continue to pay for a membership if the price increased, with an awsciates margin of errof \( 6.39 \% \). If the survey is repeated with a random sample of 272 members and the resuits are calculated in the same way, which of the following will be the most likely effect of using the larger random sample comparsinter mater arder sample? A) The margin of error will be lower. B) The margin of error wit be higher C) The estimate of the percentage of the gym's members that would contrive topay for a mentessio fite pitas increased will be lower D) The estimate of the percentage of the gym's members that would cortinue to pay for a mententio fine pice: increased will be higher:
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When using a larger sample size, we generally see an improvement in the accuracy of estimates. Specifically, as the sample size increases, the margin of error tends to decrease. This is because a larger sample provides more information about the population, reducing uncertainty in the results. Hence, in this scenario, it is likely that… A) The margin of error will be lower. Furthermore, the estimate of the percentage of gym members who would continue to pay is based on actual responses, and while a larger sample size might provide a more accurate estimate, it’s not guaranteed to move in either direction. It could remain similar, but the most significant change typically relates to the margin of error rather than the estimate itself.
