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Rahul performed an experiment using 16 windup rubber band single-propeller airplanes. He wound up the propeller a different number of times and recorded the amount of time (in seconds) that the airplane flew for each number of rotations that the propeller was wound. A regression analysis was performed and the partial computer output is given below.

The regression equation is
Time = 0.924 + 0.0462 Rotations

Predictor Coef SE Coef T P
Constant 0.9241 0.6413 1.44 0.172
Rotation 0.04625 0.01565 2.96 0.010

S= 0.5426 ; R-Sq= 38.4% ; R -Sq(adj) =34.0%

Required:
What is a 95 percent confidence interval for the slope of the regression line that relates the number of rotations the rubber band is wound and the plane's flight time?

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Answer:

0.0462 ± 2.131(0.01565)

Step-by-step explanation:

The confidence interval for the slope, :

Slope Coefficient = 0.0462

Slope Coefficient ± Margin of error

Margin of Error = Tcritical * standard error

Standard Error (rotation) = 0.01565

We use T distribution, because sample size is small ; n = 16

Tcritical at 95% ; df = n - 1 = 16 - 1 = 15

Tcritical(0.05, 15) = 2.131

Hence,

Margin of Error = 2.131(0.01565)

Slope Coefficient for rotation = 0.0462

95% Confidence interval :

0.0462 ± 2.131(0.01565)

The 95% confidence interval for the slope of the regression line is 0.0462 ± 0.0333 or (0.01284, 0.07955)

What is the margin of error?

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

Slope coefficient = 0.0462

Slope coefficient ± Margin of error

The margin of error will be given as

[tex]\rm Margin \ of \ error = T_{critical} \times standard \ error[/tex]

Standard error = 0.01565

We use T distribution because the sample size is small

[tex]\rm n = 16 \\\\T_{critical} \ at \ 95\% \ ; df = n-1 = 16- 1 = 15\\\\T_{critical} \ (0.05, 15) = 2.131[/tex]

Then we have

Margin of error = 2.131 × 0.01565

Margin of error = 0.0333

Then the 95% confidence interval will be

0.0462 ± 0.0333

More about the margin of error link is given below.

https://brainly.com/question/6979326

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