Question

The number of steps to cover the same distance was measured for 121 randomly chosen people. The sample mean is 3210 steps and the sample standard deviation is 642 steps.Assume the distribution to be normal. Round your answers to nearest integer.

Answer 1

We need to construct the 99% confidence interval for the population mean 

μ. The following information is provided:

Sample Mean $\bar X$ =3210

Standard Deviation s =642

Sample Size (N) =121

As sample size increases, the sample more closely approximates the population.so we use z confidence interval.Using ti84, invnorm the critical value for α=0.01 is  $z_c = z_{1-\alpha/2} = 2.576$

The corresponding confidence interval is computed as shown below

($\overline{X}-\frac{Z_{c}*s}{\sqrt{n}} , \overline{X}+\frac{Z_{c}*s}{\sqrt{n}}$ )

($3210-\frac{2.576*642}{\sqrt{121}} ,3210+\frac{2.576*642}{\sqrt{121}})$

(3059.665, 3360.335)

Therefore, based on the data provided, 99% confidence interval for the population mean is 3059.665<μ<3360.335, which indicates that we are 

99% confident that the true population mean μ is contained by the interval (3059.665, 3360.335).