Question

The national average of baby birth weight is roughly 3,500 kg (for full term pregnancies) with a standard deviation of 50 kg. However, in Memphis, the Health Department has raised concern that the average baby birth weight has now dropped below the national average. To explicitly investigate this, we collect the birth weight of all babies born in Shelby County from 2019-2022 (n=275) and find that the average birth weight is 3,256.7 kg and a standard deviation of 105 kg. Use hypothesis testing to determine if this is different from the national average (use significance level of 0.05).

Similarly, in addition to weight, Shelby County Health Department is concerned about average baby length. We know that the national baby birth length average is 20 inches. In our 2019-2022 cohort (n=275), we found that the Shelby County babies were on average 19.1 inches with a standard deviation of 1.2 inches.

Answer 1

Hypothesis testing with a significance level of 0.05 is used to determine if the average baby birth weight and length in Shelby County differ from the national averages, using a sample of 275 and applying a t-test.

Step-by-step explanation:

The question involves using hypothesis testing to investigate whether the average baby birth weight in Shelby County is significantly lower than the national average, and whether the average baby length is significantly different from the national average. The national average birth weight is 3,500 kg with a standard deviation of 50 kg, while the Shelby County average birth weight from data collected is 3,256.7 kg with a standard deviation of 105 kg for a sample size of n=275. For baby length, the national average is 20 inches, and in Shelby County, the average is 19.1 inches with a standard deviation of 1.2 inches, also for a sample size of n=275.

To test these hypotheses, we use a t-test since we have a sample size and a known standard deviation. The null hypothesis (H0) is that there is no difference between Shelby County and the national average. The alternative hypothesis (H1) is that the Shelby County average is less than the national average for birth weight and different from the national average for length. Using a significance level (alpha) of 0.05, we can determine whether the results are statistically significant, which would imply a lower average birth weight and different length.