The weight of 14 healthy newborn children was measured. The sample mean was 7.5 pounds with corresponding standard deviation 1.2 pounds. These babies are from one hospital and we want to test whether the babies born at this hospital are different in weight from the babies born at the hospital across town, which have a mean weight of 7.75 lbs.
5)What would be the hypotheses for this test?
5) What is the p-value for this test?
6) Using an á =0.025, what are the test statistic and rejection region?
7) What would be your conclusion?
Ho: mean = 7.5
Ha: mean ≠ 7.5
P value is arbitrary, although most experimenters use P = .05 or .01.
What test are you using?
To answer these questions, we need to conduct a hypothesis test. Here's how you can find the answers step by step:
5) The hypotheses for this test are as follows:
Null hypothesis (H0): The mean weight of babies born at this hospital is equal to the mean weight of babies born at the hospital across town (μ = 7.75 lbs).
Alternative hypothesis (Ha): The mean weight of babies born at this hospital is different from the mean weight of babies born at the hospital across town (μ ≠ 7.75 lbs).
6) To calculate the p-value, we need to use the sample mean, standard deviation, sample size, and the mean weight of the babies born at the hospital across town. Here's the formula:
t-score = (sample mean - population mean) / (sample standard deviation / √n)
Rejection region: In this case, since we are conducting a two-tailed test with α = 0.025, we need to find the critical t-values corresponding to the area of 0.025 in both tails of the t-distribution. These critical values will give us the boundaries for rejecting the null hypothesis.
7) After calculating the t-score, we can find the p-value by comparing it to the critical t-values. If the t-score falls within the rejection region, the p-value will be less than 0.025. In that case, we reject the null hypothesis. If the t-score falls outside the rejection region, the p-value will be greater than 0.025, and we fail to reject the null hypothesis.
The conclusion will depend on the p-value. If the p-value is less than 0.025, we have sufficient evidence to conclude that the weights of babies born at this hospital are different from those born at the hospital across town. If the p-value is greater than or equal to 0.025, we do not have enough evidence to conclude that there is a significant difference in the weights.