Question

Question 7. A number of studies have focused on the question of whether children born to smoker women differ physiologically from children born to non-smokers. The paper "Placental Transfer of Lead, Mercury, Cadmium, and Carbon Monoxide in Women" (Environ. Research (1978): 494-503) reported on results from one such investigation. They measured the blood-lead concentration (mg/l) for new-born babies of smoker and non-smoker mothers. The summary statistics from this study are shown in the table below:

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Group                           Sample Size                  Sample Mean                Sample Standard Deviation

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Smoker Mothers                       40                                8.6                               3.3

Non-smoker Mothers                60                                8.1                               3.5

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Do the data provide convincing evidence that the true mean blood-lead concentration for smoker’s new-born children exceeds those of born to non-smokers? ? Test at 5% level of significance using the following steps.

[1 mark] (a)      Null Hypothesis H₀ :  

                        

Alternative Hypothesis H_a :

[3 marks] (b) Compute the test-statistic

[2 mark] (c) Find the approximate P-value. What is your decision about the null hypothesis?

[1 mark] (d) State your conclusion in simple language

Answer 1

using excel>addin>phstat>two sample test

we have

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	40
Sample Mean	8.6
Sample Standard Deviation	3.3
Population 2 Sample
Sample Size	60
Sample Mean	8.1
Sample Standard Deviation	3.5
Intermediate Calculations
Population 1 Sample Degrees of Freedom	39
Population 2 Sample Degrees of Freedom	59
Total Degrees of Freedom	98
Pooled Variance	11.70878
Difference in Sample Means	0.5
t Test Statistic	0.715846
Upper-Tail Test
Upper Critical Value	1.660551
p-Value	0.237894
Do not reject the null hypothesis

(a) Null Hypothesis H0 :  smoker mothers=non-smoker mothers

                        

Alternative Hypothesis Ha : smoker mothers>non-smoker mothers

(b) the test-statistic t =0.7159

c) the approximate P-value is0.2379. since p value is greater than 005 so we do not reject Ho

(d) we do not have sufficient evidence to conclude that  the true mean blood-lead concentration for smoker’s new-born children exceeds those of born to non-smokers