Question

2) brakes are applied. An experiment was run to measure the braking distance from 60 mph for ten cars of a new model. The data (in feet ) are presented below: The braking distance of a car at a given speed is the distance it travels before it comes to a complete halt after the 161 153 175 179 173 169 187 171 172 181 a) Estimate the true mean braking distance using a 90 percent confidence interval; round the answer to ONE decimal place for FULL credit ! State the assumptions that would be considered necessary. Give interpretation of the confidence interval obtained. b) c)

Answer 1

a) The mean is obtained as

$\bar{x}=\sum_{i=1}^{n} \frac{x_{i}}{n}=\frac{161+153+...+181}{10}=172.1$

The standard deviation is given below

$S=\sqrt{\frac{\sum_{i=1}^{n}( x_{i}-\bar{x})^{2}}{n-1}}$

$=\sqrt{\frac{(161-172.1)^2+(153-172.1)^2+...+(181-172.1)^2}{10-1}}$

$=9.75$

Now 90% confidence interval is obtained as follow

$C.I=\bar{x}\pm \frac{t_{\frac{\alpha }{2}}S}{\sqrt{n}}$ Where $t_{\frac{\alpha }{2}}$ is a critical value and is equal to 1.833.

$C.I=172.1\pm \frac{1.833*9.75}{\sqrt{10}}$

$C.I=172.1\pm 5.65$

$C.I=(166.44, 177.76)$

b) The Assumption are

1. The Observation should be random and independent.

2. The data should be normally distributed.

3. Standard deviation unknown.

c) We are 90% confident that our true population mean lies between 166.44 and 177.76.