Question

A psychological researcher did a study with a sample of 84 boys and found that the meam length of time that they remained engaged with a science exhibit at a museum was 107 second. assuming that from past studies it was known that the population standard deviation was 11.7a) the best estimate for the population mean u is__b) find the 99% confidence interval of mean length of time for a recent population Please helppppppp

Answer 1

Part a)
Best estimate for the population mean u:

The population is normally distributed. The best estimate for population mean would be the mean of the sample. So the best estimate for the population mean is 107 seconds. 

Part b)
99% confidence interval:
We have the sample mean and population standard deviation so using the z distribution we can find the confidence interval.

The z value corresponding to 99% confidence interval is 2.576

The confidence interval can be found as:

$(u-z* \frac{s}{ \sqrt{n} } ,u+z* \frac{s}{ \sqrt{n} })$

Using the values in the above expression we get:

$(107-2.576* \frac{11.7}{ \sqrt{84} } ,107-2.576* \frac{11.7}{ \sqrt{84} }) \\ \\ =(103.71,110.29)$

This means the 99% confidence interval for the population mean is 103.71 to 110.29