The following table shows the weights? (in pounds) and the number of hours slept

Question

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 and interpret the results in the context of the problem. If? convenient, use technology to solve the problem. Calculate the test statistic, P valuie, and state the conclusion.

9.3.35-T Question Help 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 ?= 0.01. Then interpret the results in the context of the problem. If convenient, use technology to solve the problem. Click the icon to view more information about hypothesis testing for slope Weight,x Hours slept, y 14.8 14.5 14.114.1 13.8 13.1 13.8 12.5 8.2 10.3 9.8 7.3 6.8 11.2 11.1 15.1 Identify the null and alternative hypotheses OA, HO : M #0 HA : M#0 D. Ho: M20 HA : M#0 ?, ??: ? so HA : M#0 Calculate the test statistic. Round to three decimal places as needed.) Calculate the P-value Round to four decimal places as needed) State the conclusion. Ho. There is ? | evidence at the 10% level of significance to support the claim that there is a linear rolationship betwoon weight and number of hours slept.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 15.834815 - 0.20023207 x
Sample size: 8
R (correlation coefficient) = -0.71941991
R-sq = 0.51756501
Estimate of error standard deviation: 0.55556988

Parameter estimates:

Analysis of variance table for regression model:

Hence,

t = -2.537

P = 0.0443

Do not reject; insufficient

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 15.834815 0.81137603 ? 0 6 19.516 <0.0001 Slope -0.20023207 0.078921431 ? 0 6 -2.5371064 0.0443

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