A random sample of 90 observations produced a mean x̄ = 25.9 and a standard deviation s = 2.7. How do you find a 95% confidence interval for the population mean μ?
A 90% confidence interval for the population mean μ? A 99% confidence interval for the population mean μ?
A 90% confidence interval for the population mean μ? A 99% confidence interval for the population mean μ?
1 Answer
The 95% confidence interval for
The 90% confidence interval is
The 99% confidence interval is
Explanation:
The formula for a
#bar x+-(t_(\alpha//2," "n"-1") xx s/sqrtn)#
where
#bar x# is our sample mean,#t_(\alpha//2," "n"-1")# is the point on the#t# -distribution (with#n-1# degrees of freedom) with#100(\alpha/2)%# of the distribution's area to its right,#s# is the sample standard deviation, and#n# is the sample size.
Note: this formula assumes the population size
For a 95% confidence interval,
#100(1-0.05)%#
#=100(0.95)%#
#=95%# .
To compute the confidence interval desired, we simply plug in our values (and, in the case of the
#color(white)=bar x+-(t_(\alpha//2," "n"-1") xx s/sqrtn)#
#=25.9+-(t_(0.025,89) xx 2.7/sqrt90)#
#=25.9+-(1.987 xx 0.2846)#
#=25.9+-(0.5655)#
#=(25.33, 26.47)#
While
To obtain different confidence intervals for