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Question

# Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to study the wax by racing on the course 8 times. His 8 race times were 56.3, 65.9, 50.5, 52.4, 46.5, 57.8, 52.2, and 43.2 seconds. Should he buy the wax? Explain by using a confidence interval

Solution

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Given:

$c=\text{Confidence level}=95\%=0.95\:\:\:\:\: \color{#4257b2}(\text{Assumption})$

DESCRIPTIVE MEASURES

The mean is the sum of all values divided by the number of values:

$\overline{x}=\dfrac{56.3+65.9+50.5+52.4+46.5+57.8+52.2+43.2}{8}=\dfrac{53.1}{8}=53.1$

$n$ is the number of values in the data set.

$n=8$

The variance is the sum of squared deviations from the mean divided by $n-1$. The standard deviation is the square root of the variance:

$s=\sqrt{\dfrac{(56.3-53.1)^2+....+(43.2-53.1)^2}{8-1}}\approx 7.0285$

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