Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteering for the population of parents of school-aged children. (Round your answers to three decimal place

Answer:The 95% confidence interval would be given by (5.139;5.861)   Step-by-step explanation:1) Previous concepts A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". The margin of error is the range of values below and above the sample statistic in a confidence interval. Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". [tex]\bar X[/tex] represent the sample mean for the sample  [tex]\mu[/tex] population mean (variable of interest) s represent the sample standard deviation n represent the sample size  2) Confidence intervalAssuming that [tex]\bar X =5.5[/tex] and the ranfom sample n=1086.The confidence interval for the mean is given by the following formula: [tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1) In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by: [tex]df=n-1=1086-1=1085[/tex] Since the Confidence is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that [tex]t_{\alpha/2}=2.33[/tex] Now we have everything in order to replace into formula (1): [tex]5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139[/tex]    [tex]5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861[/tex] So on this case the 95% confidence interval would be given by (5.139;5.861)    We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.