Question

	Non-Smokers (0)	Smokers (1)	Overall
Sample size	254	72	326
Min	1587.573	1927.768	1587.573
Q1	3090.10	2863.30	3005.05
Median	3430.29	3203.50	3373.59
Q3	3742.14	3572.04	3685.44
Max	4649.322	4507.574	4649.322
Mean	3398.483	3190.109	3352.462
Standard Deviation	515.529	521.850	523.335

1. Compare the five-number summaries between the two subsamples. Briefly comment on what the summaries reveal about the location, dispersion and skewness of the birth weight distributions in the two subsamples. [2 marks]

It is well-known that, on average, smoking by the mother during pregnancy lowers the birth weight of the child. To investigate this claim statistically, you will use a hypothesis test.

3. Set up the null and alternative hypotheses. Make sure to define your notation clearly. [2 marks]

4. Verify that the Central Limit Theorem applies. Carry out the hypothesis test using the appropriate methodology, show your steps and state your conclusion. [2 marks]

5. Does it follow from the hypothesis test that children have lower birth weights because their mothers smoking during pregnancy? Explain. [2 marks]

Answer 1

(1)

(i) The mean birth weight of the child of smoking by the mother during pregnancy = 3190.109 is less than the mean birth weight of the child of non - smoking by the mother during pregnancy = 3398.483.

(ii) The variation of birth weight of the child of smoking by the mother during pregnancy = 521.850 is more than the variation of birth weight of the child of non - smoking by the mother during pregnancy = 515.529 .

(iii)

Coefficient of skewness of the distribution of birth weight of the child of smoking by the mother during pregnancy

= 3 X (Mean - Median)/ SD
= 3 X (3190.109 - 3203.50)/ 521.850

= - 0.0770

Coefficient of skewness of the distribution of birth weight of the child of non - smoking by the mother during pregnancy

= 3 X (Mean - Median)/ SD
= 3 X (3398.483 - 3430.29)/ 515.529

= - 0.1851

The distribution of birth weight of the child of smoking by the mother during pregnancy is less negatively skewed = - 0.0770    than the distribution of birth weight of the child of non - smoking by the mother during pregnancy

= - 0.1851

(2)

(i)

H0: Null Hypothesis: ( On average, smoking by the mother during pregnancy does not lower the birth weight of the child. )

HA: Alternative Hypothesis: ( On average, smoking by the mother during pregnancy lowers the birth weight of the child. ) (Claim)

(ii)

Given:

n1 = 254

n2 = 72

1 = 3398.483

2 = 3190.109

s1 = 515.529

s2 = 521.850

Pooled Standard Deviation is given by:

Test Statistic is given by:

Take

= 0.05

df = 254 + 72 - 2 = 324

From Table, critical value of t = 1.65

Since calculated value of t = 3.019 is greater than critical value of t = 1.65, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that on average, smoking by the mother during pregnancy lowers the birth weight of the child.

(iii)

It follows from the hypothesis test that children have lower birth weights because their mothers smoking during pregnancy.

Explanation:
As per the conclusion of the hypothesis test: The data support the claim that on average, smoking by the mother during pregnancy lowers the birth weight of the child.