Question #339804

A researcher wants to estimate the numbers of hours that 5 years old children spend watching television. A sample of 50 five-year old children was observed to have a mean viewing time of 5 hours. The population is normally distributed with a population standard deviation of 0.5 hours. Find the 95% confidence interval of the population mean.


1
Expert's answer
2022-05-12T08:59:05-0400

The critical value for α=0.05\alpha = 0.05 is zc=z1α/2=1.96.z_c = z_{1-\alpha/2} = 1.96.

The corresponding confidence interval is computed as shown below:


CI=(xˉzcσn,xˉ+zcσn)CI=(\bar{x}-z_c\dfrac{\sigma}{\sqrt{n}}, \bar{x}+z_c\dfrac{\sigma}{\sqrt{n}})

=(51.960.550,5+1.960.550)=(5-1.96\dfrac{0.5}{\sqrt{50}}, 5+1.96\dfrac{0.5}{\sqrt{50}})

=(4.861,5.139)=(4.861, 5.139)

Therefore, based on the data provided, the 95% confidence interval for the population mean is 4.861<μ<5.139,4.861 < \mu < 5.139, which indicates that we are 95% confident that the true population mean μ\mu is contained by the interval (4.861,5.139).(4.861, 5.139).



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