Question

In: Statistics and Probability

Please calculate the 90% Confidence Interval for the population slope in the following scenario. Suppose that...

Please calculate the 90% Confidence Interval for the population slope in the following scenario. Suppose that you collected data to determine the relationship between the amount of time a person spends online as an independent variable and the amount of money a person spends online as the dependent variable. Use the following data for questions 6, 7, 8, 9, & 10. The regression equation is = 24 + 10.1x, where x represents the number of hours a person spends online and represents the predicted amount of money that person spends online. Sample size is 6.

SSE is 300

SSR is 900

SST is 1200

Standard deviation of the sampling distribution of the sample intercept is 9.54

Standard deviation of the sampling distribution of the sample slope is 3.16

Expert Solution

Answer:-

Given ,

x = the amount of time a person spends online

y= the amount of money a person spends online

The given regression equation is,

Here given that ,

sample size n=6

SSE=300

SSR=900

SST=1200

Let as the Standard deviation of the sampling distribution of the sample intercept and,

as the Standard deviation of the sampling distribution of the sample slope

Then the 90% Confidence Interval for the population slope is given as follows,

$[Slope-t_{\alpha/2}, _(_n_-_2_)*\sigma_{slope}, Slope+t_{\alpha/2}, _(_n_-_2_)*\sigma_{slope}]$

But Slope=10.1

$t_{\alpha/2}, _(_n_-_2_)=t_{\alpha/2}, _(_6_-_2_)= 2.131847$

This valus can be obtained from t-probability table or using R-software. R-command for it is >qt(0.95,4)

Thus,

Then the 90% Confidence Interval for the population slope is,

orchestra answered 1 year ago

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