A high school basketball coach wants to see whether there is a linear relationship between player height, x , and the number of points scored in a game by basketball players in the coach’s state, y. The 96 percent confidence interval to estimate the slope of the linear regression line relating player height to points scored in a game is calculated to be (−0.432,1.844) . Assume all conditions for inference for the slope of a regression line were met. Based on the confidence interval, which of the following claims is supported by the confidence interval?
A. Each player scored at most 1.844 points in a game.
B. The average difference between actual points scored and predicted points scored is between -0.432 and 1.844.
C. There is a positive linear relationship between player height and number of points scored for basketball players in the coach's state.
D. There is a negative linear relationship between player height and number of points scored for basketball players in the coach's state.
E. It cannot be determined whether the linear relationship between player height and number of points scored for basketball players in the coach's state is positive or negative

Since 0 is in confidence interval, and negative and positive values are also, we are 96% confident in all possible answers in this interval so since true slope could be negative or positive in our interval, we cannot determine it

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astha8579 astha8579 · Answer 2 · 2022-04-29T09:03:54+02:00

It cannot be determined whether the linear relationship between player height and number of points scored for basketball players in the coach's state is positive or negative (Option E)

How to interpret the confidence interval?

Suppose the confidence interval at P% for some parameter's values is given by

[tex]x \pm y[/tex]

That means, that parameter's estimated value is P% probable to lie in the interval

[tex][x-y,x+y][/tex]

For this case, the slope of the linear regression line relating player height to points scored in a game is in the interval (−0.432,1.844) with 96% confidence.

So, we are 96% sure about the slope of the considered linear regression being in this interval. There is nothing more conveyed by this confidence interval about the slope.

Option A, B, C and D therefore are false as they state facts about slope which are not obtainable from the given data.

Thus, "it cannot be determined whether the linear relationship between player height and number of points scored for basketball players in the coach's state is positive or negative "(Option E) is corect here.

Learn more about confidence interval here:

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