For instance, a sample size of 1000 generates a confidence interval of 3.1, whic
ID: 3126042 • Letter: F
Question
For instance, a sample size of 1000 generates a confidence interval of 3.1, which implies that the estimates are more precise. On the contrary, a sample size of 500 increases the confidence interval to 4.3 and generates less accurate estimates.
How did you get the confidence intervals of 3.1 and 4.3? You need to show us how that change happened.
Actually, what you need to do is to create a confidence interval with your own information. Change the sample size twice, leaving the rest of the sample data intact, and tell us about what happened to the confidence interval when all the information remain constant except for the change in the sample size.
Explanation / Answer
For instance, a sample size of 1000 generates a confidence interval of 3.1, which implies that the estimates are more precise. On the contrary, a sample size of 500 increases the confidence interval to 4.3 and generates less accurate estimates.
How did you get the confidence intervals of 3.1 and 4.3? You need to show us how that change happened.
Actually, what you need to do is to create a confidence interval with your own information. Change the sample size twice, leaving the rest of the sample data intact, and tell us about what happened to the confidence interval when all the information remain constant except for the change in the sample size.
Let us assume population standard deviation =50
95% z value =1.96
n=1000
standard error = sd /sqrt(n) =50/sqrt(1000) =1.581
margin of error = z*se =1.96*1.581 =3.1
n=500
standard error = sd /sqrt(n) =50/sqrt(500) =2.236
margin of error = z*se =1.96*2.236 =4.3
when sample size decreases 1000 to 500, the standard error increases.
Therefore the width of confidence interval increases when sample size decreases.
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