A state politician what like to determine the average amount earned during summe

Question

A state politician what like to determine the average amount earned during summer employment by state teenagers during the past summers vacation period. She wants to have 92% confidence that the sample mean is within $50 of the actual population mean. Based past studies, she has estimated the population standard deviation = $400. What sample size is necessary to have 92 percent confidence that the sample mean will be within $50 of the actual population mean?
A.) 184 B.) 198 C.) 356 D.) 425 A state politician what like to determine the average amount earned during summer employment by state teenagers during the past summers vacation period. She wants to have 92% confidence that the sample mean is within $50 of the actual population mean. Based past studies, she has estimated the population standard deviation = $400. What sample size is necessary to have 92 percent confidence that the sample mean will be within $50 of the actual population mean?
A.) 184 B.) 198 C.) 356 D.) 425 A state politician what like to determine the average amount earned during summer employment by state teenagers during the past summers vacation period. She wants to have 92% confidence that the sample mean is within $50 of the actual population mean. Based past studies, she has estimated the population standard deviation = $400. What sample size is necessary to have 92 percent confidence that the sample mean will be within $50 of the actual population mean?
A.) 184 B.) 198 C.) 356 D.) 425

Explanation / Answer

here margin of error E =50

std deviation =400

for 92% CI critical value of z =1.7507

hence requried sample size n=(z*std deviation/E)2 =198

option B is correct.

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