Birth Weights Data Set 4 “Births” in Appendix B lists birth weights from babies born at Albany Medical Center, Bellevue Hospital in New York City, Olean General Hospital, and Strong Memorial Hospital in Rochester, New York. After partitioning the birth weights according to the hospital, we get the StatCrunch display shown here. Use a 0.05 significance level to test the claim that the different hospitals have different mean birth weights. Do birth weights appear to be different in urban and rural areas?

Birth weights were measured at four different hospitals.

The level of significance is 0.05.

Let\({\mu _1},{\mu _2},{\mu _3},{\mu _4}\)be the actual mean birth weights of babies born at Albany Medical Center, Bellevue Hospital in New York City, Olean General Hospital, and Strong Memorial Hospital,respectively.

The hypothesis is as follows:

\(\begin{aligned}{l}{H_0}:{\mu _1} = {\mu _2} = {\mu _3} = {\mu _4}\\{H_a}:\;{\rm{at}}\;{\rm{least}}\;{\rm{one}}\;{\mu _i}\;{\rm{is}}\;{\rm{different}}{\rm{.}}\end{aligned}\)

Decision rule:

• If the p-value is lesser than 0.05, reject the null hypothesis.
• If the p-value is greater than 0.05, fail to reject the null hypothesis.

The p-value in the StatCrunch output is given in the column with header p-value as 0.3167.

On comparing the p-value with 0.05, it is found to be larger. Consequently, it can be stated that the null hypothesis failed to be rejected.

Thus, it can be concluded that the mean birth weights are statistically equal among all hospitals.

The result states that the birth rates are equal among all hospitals. The difference between the birth weights in urban and rural areas cannot be analyzed using these results since the claim of the test as formulated in the hypotheses captures only the result of the population of birth weights in these four hospitals.