Babies come in all shapes and sizes when they are born, so we are often interested in what variables may help determine a baby's birthweight. In particular, we want to know if a longer gestational period (in weeks) will increase the baby's birthweight (in grams). A random sample of first-time mothers was selected and for each mother her gestational period and baby's birthweight were recorded.

1) What is the explanatory variable?

a. birth weight

b. gestational period

c. babies

d. mothers

2) what is the response variable?

a. birth weight

b. gestational period

c. babies

d. mothers

3) Check, in the context of the problem, whether the independence assumption-randomization condition is met.

For the remaining assumptions, check if they are met using the appropriate graphs. Needs name of graph and how the condition is met

4) Is the linearity assumption-straight enough condition met?

5) Is the equal variance assumption-does the plot thicken? condition met?

6) Is the normal population assumption met? check both the nearly normal condition and the outlier condition

7) State the appropriate hypotheses (Ho and Ha) in symbols only (you do not need to define the parameter)

8) Identify the test statistic and p-value from the minitab output. Remember to adjust the p-value if necessary

t=

p-value=

9) Briefly assess the strength of the evidence

10) if the assumptions are met, which of the following is the correct conclusion in the context of the question

a. we have moderate evidence that there is a linear association between mean birth weight and gestational period, for the population of all first time mothers

b. we have moderate evidence that there is a positive linear association between mean birth weight and gestational period, for the population of all first-time. mothers

c. we have moderate evidence that there is no linear association between mean birth weight and gestational period, for the population of all first-time mothers.

d. We have moderate evidence to conclude that there is a positive linear association between mean birth weight and gestational period, for the population of all first-time mothers.

Scatterplot of Birthweight vs GestPeriod Scatterplot of Birthweight vs GestPeriod 5500 5000 4500 4000 Birthweight . .. . .. 3500 .me . . .. . 3000 2500 36 37 38 39 40 41 42 43 GestPeriod Regression Analysis: Birthweight versus GestPeriod Regression Equation Birthweight = -1787 + 134.3 GestPeriod Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -1787 2527 0.71 0.483 GestPeriod 134.3 63.1 2.13 0.039 1.00 Model Summary S R-sq R-sq(adj) R-sq(pred) 519.765 8.97% 6.99% 0.86% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 1 1224654 1224654 1.53 0.039 GestPeriod 1 1224654 1224654 4.53 0.039 Error 46 12427146 270155 Lack-of-Fit 4 1312828 328207 1.24 0.309 Pure Error 42 11114318 264627 Total 7 13651800 Fits and Diagnostics for Unusual Observations Obs Birthweight Fit Resid Std Resid 3300 3047 253 0.57 13 2450 3584 -1134 -2.21 R 42 5220 3719 1501 2.94 R 47 3220 3987 -767 -1.60 X 4270 3987 283 0.59 R Large residual X Unusual XResidual Plots for Birthweight Normal Probability Plot Versus Fits 99 90 1000 Residual Percent 50 10 -1000 -1000 1000 3000 3250 3500 3750 4000 Residual Fitted Value Histogram Versus Order 12 1000 9 Residual Frequency WU -1000 -1200 -600 0 600 1200 1 5 10 15 20 25 30 35 40 45 Residual Observation Order