Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females.

x (lb) 22 27 25 24 20 15 25 21 17 24 26 22 18 19

y (lb) 122 120 116 121 130 120 145 130 130 130 130 140 110 115

In this setting we have x = 305, y = 1759, x² = 6815, y² = 222,231, and xy = 38,438.

(e) If a female baby weighs 24 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.)

________lb

(f) Find S_e. (Round your answer to two decimal places.)

S_e =

(g) Find a 95% confidence interval for weight at age 30 of a female who weighed 24 pounds at 1 year of age. (Round your answers to two decimal places.)

lower limitlb upper limitlb

(h) Test the claim that the slope of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

P-value > 0.250

0.125 < P-value < 0.250

0.100 < P-value < 0.125

0.075 < P-value < 0.100

0.050 < P-value < 0.075

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

0.0005 < P-value < 0.005

P-value < 0.0005

Conclusion

Reject the null hypothesis. There is sufficient evidence that > 0.

Reject the null hypothesis. There is insufficient evidence that > 0.

Fail to reject the null hypothesis. There is sufficient evidence that > 0.

Fail to reject the null hypothesis. There is insufficient evidence that > 0.

(i) Find an 80% confidence interval for and interpret its meaning. (Round your answers to three decimal places.)

lower limit

upper limit

Interpretation

For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval.

For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval.

For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval.

For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval.