A research firm reported that 15% of those surveyed ... Question A research firm

Question

A research firm reported that 15% of those surveyed ... Question A research firm reported that 15% of those surveyed described their health as poor, 26% as good, 40% as very good, and 19% as excellent. A health professional in Chicago wanted to determine if people in Chicago had similar feelings toward their health. In a sample of 610 people in Chicago, 70 described their health as poor, 180 as good, 220 as very good, and 140 as excellent.

Null and Alternative Hypothesis

Assumptions

Critical value

Diagram

Test Statistic

Conclusion

Explanation / Answer

H0: Question A research firm reported is valid

H1: Question A research firm reported is not valid

Assumptions:

1. Sum of the observed frequency is equal to sum of expected frequency

2. One categorical variable (i.e., the variable can be dichotomous, nominal or ordinal). Examples of dichotomous variables include gender (2 groups: male or female), treatment type (2 groups: medication or no medication), educational level (2 groups: undergraduate or postgraduate) and religious (2 groups: yes or no).

3. You should have independence of observations, which means that there is no relationship between any of the cases (e.g., participants).

4. The groups of the categorical variable must be mutually exclusive. For example, if the four groups of a categorical variable, Physical Activity Level, were "Sedentary", "Low", "Moderate" and "High", a case (e.g., a participant in an exercise study) could only be in one of these four groups (e.g., a participant could not be classified as having a "High" activity level and a "Low" activity level, but only one or the other).

5. There must be at least 5 expected frequencies in each group of your categorical variable. This is an assumption of the chi-square goodness-of-fit test and will be shown in your SPSS Statistics output when you run the test.

The critical value of the test is 7.814736 at 5% los for 3 df

Test statistic Chisquare value = 15.3113

Here chisqure value > Chisquare critical vaue, we reject H0

Thus, we conclude that research firm reported is not valid for question A

Obs Freq Exp fre Oi Proportion Ei (Oi-Ei)^2 (Oi-Ei)^2 / Ei Poor 70 0.15 91.5 462.25 5.051912568 good 180 0.26 158.6 457.96 2.887515763 very good 220 0.4 244 576 2.360655738 exellent 140 0.19 115.9 580.81 5.011302847 610 610 Total: 15.31138692

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