(6 points) When typing blood, there are four main blood groups: O, A, B and AB.
ID: 3320977 • Letter: #
Question
(6 points) When typing blood, there are four main blood groups: O, A, B and AB. It is suspected that the proportion of people with these blood groups is not equal. An X ^2 goodness of fit test is used to determine if the proportions are equal. A sample of 240 individuals is polled.
(a) State the null hypothesis of this test.
(b) How many degrees of freedom does the test statistic have?
(c) The value of the test statistic is X^2 = 7.859 and the table shows that the p-value = 0.049. Is there evidence that the proportions of blood groups ARE equal, at the 5% level?
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: The proportion of people with these blood groups not equal..
Alternative hypothesis: The proportion of people with these blood groups is not equal.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.
Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.
2 = [ (Oi - Ei)2 / Ei ]
2 = 7.859
where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, Ei is the expected frequency count for level i, Oi is the observed frequency count for level i, and 2 is the chi-square test statistic.
We use the Chi-Square Distribution Calculator to find P(2 > 7.859) = 0.049
Interpret results. Since the P-value (0.049) is less than the significance level (0.05), we cannot accept the null hypothesis.
We do not have sufficient evidence in the favor of the claim that proportions of blood groups are equal.
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