A psychological study found that the mean length of time that boys remained enga

Question

A psychological study found that the mean length of time that boys remained engaged with a science exhibit museum was 107 seconds with a standard deviation of 117 seconds. Suppose a random sample of 36 has a mean length of 107 seconds and assume the standard deviation of all boys remained engaged with science exhibit at a museum is 117 seconds. A. Verify the requirement for constructing the confidence interval estimate of the mean length of time that all boys remained engaged with a science exhibit at a museum. B. Construct and interpret a 95% confidence interval estimate of the mean length of time that allboys remained engaged with a science exhibit at a museum. A psychological study found that the mean length of time that boys remained engaged with a science exhibit museum was 107 seconds with a standard deviation of 117 seconds. Suppose a random sample of 36 has a mean length of 107 seconds and assume the standard deviation of all boys remained engaged with science exhibit at a museum is 117 seconds. A. Verify the requirement for constructing the confidence interval estimate of the mean length of time that all boys remained engaged with a science exhibit at a museum. B. Construct and interpret a 95% confidence interval estimate of the mean length of time that allboys remained engaged with a science exhibit at a museum. A. Verify the requirement for constructing the confidence interval estimate of the mean length of time that all boys remained engaged with a science exhibit at a museum. B. Construct and interpret a 95% confidence interval estimate of the mean length of time that allboys remained engaged with a science exhibit at a museum.

Explanation / Answer

a) as sample size is greater then 30 and population standard deviaiton is given we can use standard normal distribution to compute confidence interval from central limit theorum

b) for std error of mean =std deviaiton/(n)1/2 =19.5

for 95% CI, z=1.96

hence 95% confidence interval =sample mean -/+ z*Std errror =68.7807 ; 145.2193

above interval gives 95% confidence to contain true population mean   mean length of time that boys remained engaged with a science exhibit museum

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