Answer:
The construct of the 95% confidence interval estimate of the mean age of all race car drivers is 26.65 < [tex]\bar x[/tex] < 37.35
Step-by-step explanation:
The formula for confidence interval (C. I.) for a sample mean is given as follows;
[tex]CI=\bar{x}\pm t_{\alpha/2, n-1} \dfrac{s}{\sqrt{n}}[/tex]
Where:
[tex]\bar x[/tex] = Sample mean
s = Sample standard deviation
n = Sample size = 6
[tex]t_{\alpha /2}[/tex] = The test statistic at the given confidence level
n - 1 = The degrees of freedom 5
The sample mean [tex]\bar x[/tex] = ∑x/n = (32 + 40 + 27 + 36 + 29 + 28)/6 = 32
The standard deviation is given as follows;
[tex]s = \sqrt{\dfrac{\Sigma (x - \bar x)^2 }{n - 1} } = 5.099[/tex]
At 95% confidence level, α = 0.05, therefore α/2 = 0.025 and we look for [tex]t_{0.025}[/tex] and 5 degrees of freedom, [tex]t_{0.025}[/tex] = 2.571
When we put in the values, we have;
[tex]CI=32\pm 2.571 \times \dfrac{5.099}{\sqrt{6}}[/tex]
Which gives;
26.65 < [tex]\bar x[/tex] < 37.35
The construct of the 95% confidence interval estimate of the mean age of all race car drivers = 26.65 < [tex]\bar x[/tex] < 37.35.
