Problem 3: Airline pilots face the risk of progressive hearing loss due to the n

Question

Problem 3: Airline pilots face the risk of progressive hearing loss due to the noisy cockpits of most jet aircraft. Much of the noise comes from air roar which increases at high speeds rather than from the engines. The cockpit noise (in decibels) was measured to the left ot pilots ear on 60 randomly selected flights of one type of aircraft. The computer output below shows the results from a regression model in which the cockpit noise level was predicted by the air speed (in mph). Assume the conditions of the linear regression model are satisfied within the range of air speeds tested. Regression Analysis: Noise versus Speed The regression equation is Noise 65.6 + 0.0734 Speed Coef SE Coef 95% CI T-Value P-Value Predictor Constant 65.624 10.42 44.77, 86.47) 6.28 0.000 Speed 0.073417 0.03098 (0.0115, 0.1354) 2.37 0.021 R-Sq= 8.858 R-Sq (adj) 7,288 . S= 11.4088 a. According to the regression line, what is the estimated mean cockpit noise for a plane sitting on the runway, not moving, with its engines running? b. Test the hypothesis that the intercept is 0 using a significance level of 0.05

Explanation / Answer

Part (a) : When plane is sitting on the runway, not moving, air speed is zero. Therefore, From the regression equation, When Speed = 0, we get Noise = 65.624; which is the estimated value of the constant in the regression equation. Therefore, the estimated mean cockpit noise for a plane sitting on a runway is 65.624

Part (b): The intercept refers to the Constant term in the regression equation. For testing the given hypothesis, the prescribed level of significance is 0.05. Now in the regression estimation data for the "Constant" shows its actual value as 65.624 along with P-value of 0.000. In general, P-value is interpreted as the Observed level of significance.

Whenever we get : Observed Significance Level < Prescribed Significancle Level, we reject the null hypothesis. In this case, 0.0000 (observed) < 0.05 (prescribed) , therefore we reject the null hypothesis that "The intercept is 0".

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