650-Q3

A courier service in NYC advertises that its average delivery time is less than 6 hours for local deliveries. A random sample of the amount of time this courier takes to deliver packages to an address across town produced the following delivery times (rounded to the nearest hour)

7, 3, 4, 6, 10, 5, 6, 4, 3, 8

Assuming that the daily output is normally distributed, is there sufficient evidence to support the courier's advertisement? (Use a significance level of 0.05).

1. State the null and alternative hypothesis that best tests the hypothesis of interest. Be sure to pay attention to whether this should be a 1-tailed or a 2-tailed test.
2. Carry out this test, and state whether you reject or fail to reject the null hypothesis. In computing the test statistic, be sure to indicate whether you are using "t" or "z".Use the precise critical value of the "t" or "z" you use, not an approximation.
3. Given your answer to part b., are you vulnerable to a Type I or Type II error?Explain why, in a single sentence.