RESEARCH METHODOLOGY

STATISTICAL TECHNIQUES AND TOOLS

CONFIDENCE INTERVALS

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A population has a standard deviation of = 17.3. How large of a sample must be drawn so that a 95% confidence interval for µ will have a Margin of Error equal to 1.4?
A
586.6
B
587
C
586
D
585
Explanation: 

Detailed explanation-1: -Where, , n, , n, is the level of significance, sample size and population standard deviation respectively. Therefore, the sample size of 1204 must be drawn so that a 95% confidence interval for mean will have a margin error of error equal to 1.

Detailed explanation-2: -To be 95% confident that the true value of the estimate will be within 5 percentage points of 0.5, (that is, between the values of 0.45 and 0.55), the required sample size is 385. This is the number of actual responses needed to achieve the stated level of accuracy.

Detailed explanation-3: -To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1, 000.

Detailed explanation-4: -We want to construct a 95% confidence interval for with a margin of error equal to 4%. Because there is no estimate of the proportion given, we use for a conservative estimate. This is the minimum sample size, therefore we should round up to 601.

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