Problem:Hypothesis tests for the correlation coefficient and the slope of the least-squares regression line
Newburg Park, Florida is a popular, beach resort town. Property values are fairly high there and, as such, are rather well studied. One topic of study has been the relationship between housing prices and distance from the beach.
For a recent sample of 16 houses sold in Newburg Park in the past year, the least-squares regression equation relating the variables house price (denoted by x , in thousands of dollars) and distance from the beach (denoted by y , in miles) was yˆ=300.83-5.47x . The standard error of the slope of the least-squares regression line was approximately 2.48 .
Based on this information, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope β1 . (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test.
Answer the following:
What are the null and alternative hypotheses?
What type of test statistic is used (Z, t, f, or Chi square)?
What is the value of the test statistic (Round to at least 3 decimal places)?
What is the p-value (Round to at least 3 decimal places)?