Blood Type A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown:

f. Contact a local hospital and ask them the percentage of the population that is blood type O. Why might the results differ?

Verified step by step guidance

1. Step 1: Count the number of patients with blood type O in the sample. Go through each entry in the table and tally how many times 'O' appears.
2. Step 2: Calculate the sample proportion of blood type O by dividing the count of blood type O patients by the total number of patients sampled (which is 50). Use the formula: \(\text{Proportion of O} = \frac{\text{Number of O patients}}{50}\).
3. Step 3: Contact the local hospital to obtain the percentage of the population that has blood type O. This percentage represents the population proportion of blood type O.
4. Step 4: Compare the sample proportion from the phlebotomist's data to the population proportion from the hospital. Consider reasons why these two values might differ, such as sampling variability, sample size, or differences in the population from which the sample was drawn.
5. Step 5: Reflect on factors like sampling bias, demographic differences, or random chance that can cause the sample proportion to differ from the true population proportion.

Key Concepts

Sampling Variability

Sampling variability refers to the natural differences that occur when different samples are taken from the same population. Because the phlebotomist's sample is random and relatively small (50 patients), the observed blood type proportions may differ from the true population percentages due to chance.

Population vs. Sample

A population includes all individuals of interest, while a sample is a subset selected for study. The hospital's reported blood type percentages represent the population, which is typically larger and more comprehensive than the phlebotomist's sample, leading to potential differences in results.

Bias and Representativeness

Bias occurs when a sample does not accurately represent the population. Factors like location, demographics, or sampling method can cause the phlebotomist's sample to differ from the hospital's data, affecting the observed blood type distribution and causing discrepancies.