Problem 6: Multiple Choice Suppose a random sample of 1,220 U.S. adults were ask

Question

Problem 6: Multiple Choice Suppose a random sample of 1,220 U.S. adults were asked about their opinion regarding federal spending on public education. Respondents were asked whether federal spending on public education was (a) too low, (b) adequate, or (c) too high. Respondents were classified by income level. Choose the correct hypotheses to test whether there is an association between the response to the question and income level. Justify your answer a. Ho Among U.S. adults, opinions about federal spending on education and income level are independent. Ha Among U.S. adults, opinions about federal spending on education and income level are associated. b. Ho : Among U.S. adults, opinions about federal spending on education and income level are associated. Ha Among U.S. adults, opinions about federal spending on education and income level are independent c. H There is no difference between the proportions of U.S. adults who responded (a), (b) or (c) to the opinion question. Ha : There is a difference between the p S. adults who responded (a), (b) or (c) to the opinion question. All of the above None of the above

Explanation / Answer

Solution:

     We are given that : a random sample of 1220 U.S. adults were asked about their opinion regarding federal spending on public education whether it is too low , adequate or too high and these respondents were classified by their income level.

   We would like to test if there is an association between the response to the question and income level and thus we have to state null hypothesis H0 and alternative hypothesis Ha.

That is we have to test if the response to the question and income level   are independent or not independent ( associated). For testing independence or association between two attributes , we use Chi-square test of independence and in the null hypothesis we always state that two attributes are independent whereas in alternative hypothesis we state two attributes are not independent ( that is associated).

Thus correct hypothesis are:

H0: Among the U.S. adults, opinions about federal spending on education and income level are independent.

Vs

Ha: Among the U.S. adults, opinions about federal spending on education and income level are associated.

Thus option a) is correct.

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