Question

according to theory, blood types in the general population occur in the following proportions: 46% 0, 40% a, 10% b, and 4% ab. anthropologists come upon a previously unknown civilization living on a remote island. a random sampling of blood types yields the following counts: 77 0, 85 a, 23 b, and 15 ab. is there sufficient evidence to conclude that the distribution of blood types found among the island population differs from that which occurs in the general population? (a) the data prove that blood type distribution on the island is different from that of the general population (b) the data prove that blood type distribution on the island is not different from that of the general population (c) the data give evidence at the 1% significance level that blood type distribution on the island is different from that of the general population. (d) the data give evidence at the 5% significance level, but not at the 1% significance level, that blood type distribution on the island is different from that of the general population. (e) the data do not give evidence at the 5% significance level that blood type distribution on the island is different from that of the general population.

Answer 1

To determine if the blood type distribution on the island is different from the general population, a chi-square goodness-of-fit test can be conducted. The null hypothesis assumes that the distributions are the same, while the alternative hypothesis suggests they are different. By comparing the calculated chi-square test statistic to the critical value at different significance levels, it can be determined if there is enough evidence to conclude a difference in the blood type distributions.

Step-by-step explanation:

To determine whether the distribution of blood types on the remote island differs from the general population, we can conduct a chi-square goodness-of-fit test. The null hypothesis is that the observed distribution of blood types on the island is the same as the expected proportions in the general population. The alternative hypothesis is that the observed distribution is different.

We calculate the expected counts by multiplying the total count by the proportions in the general population. We then calculate the chi-square test statistic using the formula: (observed count - expected count)^2 / expected count. We sum up the test statistics for each blood type and compare it to the critical value from the chi-square distribution. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the distribution is different.

In this case, the calculated chi-square test statistic is larger than the critical value at both the 1% and 5% significance levels. Therefore, we can conclude that there is sufficient evidence to suggest that the distribution of blood types on the island is different from that of the general population. The correct answer is (d) the data give evidence at the 5% significance level, but not at the 1% significance level, that blood type distribution on the island is different from that of the general population.