6. A manufacturer of batteries for electric cars claims that an hour of charge can power a certain model of car to travel for an average of 123 miles. An electric car company and a consumer, Hopcyn, both wish to test the validity of the manufacturer's claim.

1. Explain why Hopcyn may want to use a one-sided test and why the car company may want to use a two-sided test. To test the validity of this claim, Hopcyn collects data from a random sample of 90 drivers of this model of car to see how far they travelled, \(X\) miles, on an hour of charge. He produced the following summary statistics. $$\sum x = 11007 \quad \sum x ^ { 2 } = 1361913$$
2. 1. Assuming Hopcyn uses a one-sided test, state the hypotheses.
   2. Test at the \(5 \%\) significance level whether the manufacturer's claim is correct.