# Testing a Statistic without standard deviation?

1. Nov 30, 2008

### KatieLynn

1. The problem statement, all variables and given/known data

Due to the expense involved, car crash tests often use small samples. When 5 BMW cars are crashed under standard conditions, the repair costs (in dollars) are as shown in accompanying list. Use 0.05 significance level to test the claim that the mean for all BMW cars is less than \$1000.

797, 571, 904, 1147, 418

2. Relevant equations

3. The attempt at a solution

I don't understand how I can do this problem with out being given the standard deviation. Any suggestions?

2. Nov 30, 2008

### Staff: Mentor

I wouldl suggest using the Student t test. The statistic t is given by
$$t = \frac{\bar{y} - \mu_0}{\frac{s}{\sqrt{n}}}$$

In the above, s is the sample st. dev.
$$s = \sqrt{\frac{n \sum_{i = 1}^n x_i^2 -(\sum_{i = 1}^n x_i)^2}{n(n - 1)}}$$