Question: A carpet retailer wants to start a new ad campaign based on delivery time, stating that it will take no more than 15 days to deliver carpet. A random sample of 20 recent deliveries is taken, assuming the delivery time for carpet is normally distributed:

1. State the null and alternative hypothesis to determine whether they can deliver on their promise to deliver in 15 or fewer days .
2. State the decsion rule for = 0.01
3. Below is the sample of 20 deliveries, time expressed in days:

   17.2	15.2
   17.6	14.8
   18.2	14.2
   18.7	13.7
   19.2	13.2
   19.8	12.6
   20.2	12.2
   21.0	11.4
   21.2	11.2
   21.4	11.0

   
   Calculate the mean and standard deviation for the sample of 20.
4. What can be concluded about delivery time, why?
5. What type of error could they be making and what is the probability (or range of probability) for making that error?

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