In: Statistics and Probability
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 Ha :
[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
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