Question

In Norway, the distribution of birth weights for full-term infants whose gestational age is 40 weeks is approximately normal with mean μ= 3500 grams. We wish to determine if the birth weights of full-term babies whose mothers smoked throughout pregnancy is less than those of non-smoking mothers. A sample of 17 babies born to mothers who smoked is collected. The sample mean is 3297 grams and the sample standard deviation is 430 grams.

Test your hypothesis at the α = 0.05 level and explain what the results mean.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   < 3500

H_a :    3500

= 3297

= 3500

s = 430

n = 17

degrees of freedom = n = 1 = 17 - 1 = 16

Test statistic = t

= ( - ) / s / n

= (3297 - 3500) / 430 / 17

= -1.95

Test statistic = -1.95

P-value = 0.0345

= 0.05

P-value <

Reject the null hypothesis .

There is enough evidence to suggest that the birth weights of full-term babies whose mothers smoked throughout pregnancy is less than those of non-smoking mothers .