Question

a.) find the test statistic, t. round three decimal places

b.) calculate the P-value. round four decimal places

The following table shows the weights (in pounds) and the number of hours slept in a day by a random sample of infants. Test the claim that M 0. Use a-0.1. Then interpret the resuts in the context of the problem convenient, use technology to solve the problem Click the icon to view more information about hypothesis testing for slope. Weight, x Hours slept, y 82 10.2 9.9 7.1 69 11.2 109 15.1 14.8 14.5 14.1 13.8 13.2 13.8 14.1 12.5 Caloulate the test statistic (Round to three decimal places as needed) Calculate the P-value P- (Round to four decimal places as needed)

Answer 1

We will be using R to estimate the linear regression equation and test the significance of the slope.

> x = c(8.2, 10.2,9.9,7.1,6.9,11.2,10.9,15.1)
> y = c(14.8,14.5,14.1,14.1,13.8,13.2,13.8,12.5)
> m = lm(y~x)
> summary(m)

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-0.65611 -0.33942 -0.08707 0.33271 0.70238

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 15.83294 0.78100 20.273 9.36e-07 ***
x -0.19954 0.07624 -2.617 0.0397 *
---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5366 on 6 degrees of freedom
Multiple R-squared: 0.5331,   Adjusted R-squared: 0.4553
F-statistic: 6.851 on 1 and 6 DF, p-value: 0.03973

From the summary output,

test statistic, t = -2.617

P-value = 0.0397