Testing a Statistic without standard deviation?

[KatieLynn]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I don't understand how I can do this problem without being given the standard deviation. Any suggestions?

 

[Mark44]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I don't understand how I can do this problem without being given the standard deviation. Any suggestions?

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.
$$s = \sqrt{\frac{n \sum_{i = 1}^n x_i^2 -(\sum_{i = 1}^n x_i)^2}{n(n - 1)}}$$