XR18-75 In recent years, fishermen have suffered financial hardship because of shortened fishing…

XR18-75 In recent years, fishermen have
suffered financial hardship because of shortened fishing seasons, reduced
catches and lower market prices. Moreover, fishermen have complained about
price fluctuations and have called for a system of minimum prices. One
suggestion made was that the size of the catch had an immediate impact on
prices, and that this relationship should be clarified before potential
solutions were discussed. To investigate this issue, a random 12-week period
was selected to study the price of fish versus the average daily catch.
The data were collected for analysis
»

XR18-75 In recent years, fishermen have
suffered financial hardship because of shortened fishing seasons, reduced
catches and lower market prices. Moreover, fishermen have complained about
price fluctuations and have called for a system of minimum prices. One
suggestion made was that the size of the catch had an immediate impact on
prices, and that this relationship should be clarified before potential
solutions were discussed. To investigate this issue, a random 12-week period
was selected to study the price of fish versus the average daily catch.
The data were collected for analysis and recorded. Part of the data are
presented below.

a Determine the sample regression line that
shows the price per kilogram as a function of average daily catch.

b Calculate the standard error of estimate.
What does this value tell you about the relationship between the two variables?

c Do these data provide sufficient evidence
at the 5% significance level to allow you to conclude that large catches result
in lower prices?

d Calculate the coefficient of
determination. What does this value tell you about the relationship between the
two variables?

e Find a 90% confidence interval estimate
for the expected value of the price per kilogram if the daily catch is 75000
kg.

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