Question 1194422: a researcher wants to know the mathematical performance of th grade 11 statistics students under a specific teaching strategy. she wants to estimate the population mean within an error of 3% of its true value and a confidence level of 95%. previous studies showed that the standard deviation is q=0.36. find the required sample size to estimate the population mean.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
At 95% confidence, the critical z value is about z = 1.960
You would use a reference table to determine this value.
sigma = 0.36 = standard deviation
E = 0.03 = the 3% error desired
We want to hit 0.03 exactly or be below this.
Put another way, we want to be within 3% of the error.
n = minimum sample size
n = (z*sigma/E)^2
n = (1.96*0.36/0.03)^2
n = 553.1904
n = 554
Always round UP to the nearest whole number when it comes to minimum sample size problems like this. It doesn't matter that 553.1904 is closer to 553 than it is to 554.
Why round up? Let's try plugging n = 553 into the margin of error formula
E = z*sigma/sqrt(n)
E = 1.960*0.36/sqrt(553)
E = 0.030005 approximately
We're slightly over the target of E = 0.03; we want to be at this or below.
Now try n = 554
E = z*sigma/sqrt(n)
E = 1.960*0.36/sqrt(554)
E = 0.029978 approximately
Now we're below the target of E = 0.03
Side note: As you can probably guess, as the sample size (n) goes up, the margin of error (E) goes down. This is when the z value and sigma are held constant.
Answer: 554
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