Question

1. a) A fishery sent a shipment with several boxes of salmon to a large seafood restaurant. The restaurant’s quality manager inspected one randomly selected box containing 16 salmon. Summary statistics for the weight (in lbs) of the salmon in the inspected box are given below.

Mean 5.1

Median 5.1

Lower quartile 4.5

Upper quartile 6.1

Standard deviation 1.4

Min 3.2

Max 8.1

i. Compute the lower fence (lower bound) for determining outliers using the IQR Rule. Round to 2 decimal places.

ii. According to the IQR Rule, the salmon with the lowest weight in the box is an outlier. True False (circle your choice)

iii. Choose the most appropriate statistic to measure the spread of this distribution and interpret its value in the context of the question.

b) The restaurant will reject the entire shipment if the average weight of the salmon is under 6 lbs. Test this claim using the sample of salmon in the inspected box. Assume the standard deviation of entire shipment is 1.6 lbs.

i. Let µ represent the parameter of interest in this study. Define µ.

ii. The null hypothesis is H0: _________ lbs.

iii. The alternative hypothesis is Ha: __________ lbs.

iv. Compute the test statistic. Round to 2 decimal places.

v. Compute the p-value. Round to 4 decimal places.

vi. Make an appropriate conclusion using a 5% significance level. vii. Based on your conclusion from the significance test, the restaurant should reject the shipment and send it back to the fishery. True False (circle your choice)

viii. Did you make any assumptions for this significance test that were not already stated in the question?

Answer 1