The lower limit of a confidence interval at the 95% level of confidence for the population proportion if a sample of size 100 had 30 successes is:

A) 0.3898
B) 0.2102
C) 0.2959
D) 0.3041
E) 0.3126

Question

The lower limit of a confidence interval at the 95% level of confidence for the population proportion if a sample of size 100 had 30 successes is:A)  0.3898B)  0.2102C)  0.2959D)  0.3041E)  0.3126

Frances Rangel · Accepted Answer

Final Answer : B, Explanation :  The sample proportion (p-hat) is 30/100 = 0.3. Using the formula for the confidence interval for a proportion, the lower limit is calculated as p-hat - Z*(sqrt(p-hat*(1-p-hat)/n)), where Z is the Z-score for 95% confidence (approximately 1.96). This calculation gives approximately 0.2102.

The lower limit of a confidence interval at the 95% level of confidence for the population proportion if a sample of size 100 had 30 successes is:

A) 0.3898
B) 0.2102
C) 0.2959
D) 0.3041
E) 0.3126

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