Respuesta :
Answer:
a) [tex]\pm 2.2527[/tex]
b) n = 169
Step-by-step explanation:
We are given the following information:
Sample mean, [tex]\bar{x}[/tex] = 13.2 mp
Sample size, n = 36
Alpha, α = 0.10
Sample standard deviation, s = 8 mph
90% Confidence interval: (10.95, 15.45)
a)
[tex]\text{Margin of error}} = \text{Critical value}\times \text{Standard error of the statistic}\\ = t_{critical}\times \displaystyle\frac{s}{\sqrt{n}}[/tex]
[tex]t_{critical}\text{ at degree of freedom 35 and}~\alpha_{0.10} = \pm 1.689572[/tex]
Putting the values, we get,
[tex]\text{Margin of error} = t_{critical} \times \displaystyle\frac{s}{\sqrt{n}}\\\\= \pm 1.689572\times \frac{8}{\sqrt{36}} = \pm 2.2527[/tex]
b) [tex]\text{Margin of error} = \pm 1[/tex]
[tex]t_{critical} \times \displaystyle\frac{s}{\sqrt{n}}\\\\\Rightarrow \pm 1.689572\times \frac{8}{\sqrt{n}} = \pm 1\\\\\Rightarrow \sqrt{n} = \frac{\pm 1.689572\times 8}{ \pm 1} = 13.5165 \approx 13\\\\\Rightarrow \bold{n = 169}[/tex]
