Question

Based on the National Center of Health Statistics, the proportion of babies born at low birth weight (below 2,500 grams) in the United States is roughly .078, or 7.8% (based on all the births in the United States in the year 2002). A study was done in order to check whether pregnant women exposed regularly to second hand smoke increases the risk of low birth weight. In other words, the researchers wanted to check whether the proportion of babies born at low birth weight among women who were exposed regularly to second hand smoke during their pregnancy is higher than the proportion in the general population. The researchers followed a sample of 400 women who had been exposed regularly to second hand smoke during their pregnancy and recorded the birth weight of the newborns. Based on the data, the p-value was found to be 0.119.

1/ Write down the null and alternative hypotheses (H_oand H_a) that are being tested here.

Important: It is VITAL that your practice this on your own. Please write down both of your hypothesis first in your notes and then copy them here.

2/ Based on the p-value, what is your conclusion (use .05 significance level)?

a) Since the p-value is .119, it is extremely unlikely that we would get data like those observed if, indeed, second-hand smoking does not increase the risk of low birth weight (H₀ is true). In particular, since the p-value is not less than .05, we cannot conclude that the data do not provide enough evidence to conclude that second-hand smoking increases the risk of low birth weight.

b) Since the p-value is .119, it IS extremely unlikely that we would get data like those observed if, indeed, second-hand smoking does not increase the risk of low birth weight (H₀ is true). In particular, since the p-value is not less than .05, we conclude that the data do not provide enough evidence to conclude that second-hand smoking increases the risk of low birth weight.

c) Since the p-value is .119, it is NOT extremely unlikely that we would get data like those observed if, indeed, second-hand smoking does not increase the risk of low birth weight (H₀ is true). In particular, since the p-value is not less than .05, we conclude that the data do provide enough evidence to conclude that second-hand smoking increases the risk of low birth weight.

d) Since the p-value is .119, it is NOT extremely unlikely that we would get data like those observed if, indeed, second-hand smoking does not increase the risk of low birth weight (H₀ is true). In particular, since the p-value is not less than .05, we conclude that the data do not provide enough evidence to conclude that second-hand smoking increases the risk of low birth weight.

3/ Can we conclude that the results of this study provide evidence that being exposed to second hand smoke while pregnant does not increase the risk of low birth weight?

a) Yes. In hypothesis testing we can conclude that we accept H₀ (or that H₀ is true) if there is enough evidence.

b) It depends. Sometimes you can, and sometimes you cannot. We don't have enough information in this example to know for sure.

c) No. In hypothesis testing we can never conclude that we accept H₀ (or that H₀ is true). All we can say (in case we do not get a small p-value) is that we do not have enough evidence to reject H₀.

Answer 1

#1) Claim : The proportion of babies born at low birth weight among women who were exposed regularly to second hand smoke during their pregnancy is higher than 0.078

P = 0.078 vs P > 0.078

#2) Based on the p-value, what is your conclusion

d) Since the p-value is .119, it is NOT extremely unlikely that we would get data like those observed if, indeed, second-hand smoking does not increase the risk of low birth weight (H0 is true). In particular, since the p-value is not less than .05, we conclude that the data do not provide enough evidence to conclude that second-hand smoking increases the risk of low birth weight.

#3 ) Conclusion :

c) No. In hypothesis testing we can never conclude that we accept H0 (or that H0 is true). All we can say (in case we do not get a small p-value) is that we do not have enough evidence to reject H0.