A seafood-sales manager collected data on the maximum daily temperature, T, and the daily revenue from salmon sales, R, using sales receipts for 30 days selected at random. Using the data, the manager conducted a regression analysis and found the least-squares regression line to be Rˆ=126+2.37T. A hypothesis test was conducted to investigate whether there is a linear relationship between maximum daily temperature and the daily revenue from salmon sales. The standard error for the slope of the regression line is SEb1=0.65. Assuming the conditions for inference have been met, which of the following is closest to the value of the test statistic for the hypothesis test?

a. t=0.274

b. t=0.65

c. t=1.54

d. t=3.65

e. t=193.85

The closest value of the test statistic for the hypothesis test is 3.65 if the least-squares regression line to be Rˆ=126+2.37T option (d) is correct.

What is a regression line?

A regression line is a graph that illustrates the pattern of a group of statistics. In other words, it shows the data's best pattern.

We have a least-squares regression line to be:

R^ = 126+2.37T

A hypothesis test was conducted to investigate whether there is a linear relationship between maximum daily temperature and the daily revenue from salmon sales.

Using a T-test to find the significance of the slope coefficient is measured:

[tex]\rm t = \frac{b}{SE}[/tex]

Here SE = 0.65

b = 2.37

Put this value in the above expression, we get:

[tex]\rm t = \frac{2.37}{0.65}[/tex]

t = 3.6461 or

t = 3.65

Thus, the closest value of the test statistic for the hypothesis test is 3.65 if the least-squares regression line to be Rˆ=126+2.37T option (d) is correct.

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