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A total of 498 participants responded to a survey questionnaire. I want to be ascertain that the sample size of 498 reflects the opinions of the true population (say 1,000,000).

I used an online calculator that shows that the margin of error is 4% population size: 1000,000 confidence level (%): 95 Your sample size: 498

The margin of error is 4% (online calculator)

Manual Calculation: Group A: 123, Group B: 70, Group C:37, Group D:40, Group E:74, Group F:15, Group G:15, Group H:15, Group I:28, Group J:81

Count, N: 10 Sum, Σx: 498 Mean, x̄: 49.8 Variance, s2: 1299.2888888889 std deviation, s = √1299.2888888889 s = 36.04565006889

Standard Error, sx̄ = s / √N = 36/ √10 =11.39863539591

Margin of Error = critical value x Standard Error = 1.96 x 11.39863539591 = 22.341

Please advise why the margin of error (using manual calculation) results in 22.341

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  • $\begingroup$ Please tell us what you think a "margin of error" might mean with ten groups. What exactly are you trying to estimate here?? $\endgroup$
    – whuber ♦
    Commented Nov 30, 2022 at 23:25
  • $\begingroup$ Referring to the online calculator at surveymonkey.com/mp/margin-of-error-calculator it shows that the margin of error is 4% based on the total sample size of 498 participants. In the above calculation, N=10; Does N (total number of values) need to be 498? If N=498, then Standard Error, sx̄ = s / √N = 36.04565006889/ √498 =1.61524; Margin of Error is 1.96 x 1.61524 = 3.17 >>>> which is close to 4% (with a 95% confidence interval of critical value 1.96). Is that correct? $\endgroup$
    – Vyas
    Commented Dec 1, 2022 at 0:15
  • $\begingroup$ I'm sorry, but I find it impossible to tell what you're doing. You need to explain what your groups mean and what you are trying to learn from this survey. $\endgroup$
    – whuber ♦
    Commented Dec 1, 2022 at 0:22
  • $\begingroup$ Sorry, I was not explicit enough. We surveyed participants from the gaming sector comprising developers, designers, narrators, programmers, etc. These are the groups. The goal is to show that the sample size of 498 (by combining all the groups) reflects the true population of the gaming industry (100,000+). I guess I was confused above in my preliminary expose about denoting N. I illustrated N = 10 (number of groups) rather than N=498 (total sample size) $\endgroup$
    – Vyas
    Commented Dec 1, 2022 at 1:14
  • $\begingroup$ We can also say that if the margin of error is small, the chosen sample represents the opinions of the true population with more confidence. $\endgroup$
    – Vyas
    Commented Dec 1, 2022 at 1:31

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