Hi @Pushpen_Bikash_Goala !!
The p-value (0.03 in this case) represents the probability of observing data as extreme as or more extreme than the observed data, assuming that the null hypothesis (H0) is true. If the p-value is small (typically less than the significance level, alpha, which is often set at 0.05), it suggests that the observed data is unlikely to occur under the assumption that the null hypothesis is true. In such cases, we reject the null hypothesis in favor of the alternative hypothesis (Ha).
Now, let’s address the statement:
“If smoking has no effect on the duration of pregnancy, there is a 3% random chance that a sample of 40 smokers will have pregnancies lasting less than 260 days.”
Explanation: The statement is valid and correctly interprets the p-value. Here’s how to understand it:
- Null Hypothesis (H0): μ = 266 (Smoking has no effect on pregnancy duration).
- Alternative Hypothesis (Ha): μ < 266 (Smoking has an effect, leading to shorter pregnancy duration).
With a p-value of 0.03, it means that if the null hypothesis (H0) were true (smoking has no effect on pregnancy duration), there would be only a 3% chance of obtaining a random sample of 40 smokers with a mean pregnancy duration of less than 260 days.
In other words, the observed sample mean of 260 days is unlikely to occur by random chance if the null hypothesis were true. The small p-value (0.03) suggests that there is strong evidence to reject the null hypothesis and support the alternative hypothesis, indicating that women who smoke may have a higher risk of shorter pregnancies compared to the general population (mean pregnancy duration of 266 days).
Happy Learning 
