Chapter 12: Q. 12.2 (page 484)
How do you identify different chi-square distributions?
The number of degrees of freedom is used to identify the different chi-square distributions.
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A poll conducted by Gallup asked American adults about vegetarianism. This problem is based on that poll. Of independent random samples of men and women, of the men and of the women said they were vegetarians. At the significance level do the data provide sufficient level do the data provide sufficient evidence to conclude that a difference exists in the proportions of male and female vegetarians?
Part (a): Use the two-portions z-test to perform the required hypothesis test.
Part (b): Use the chi-square homogeneity test to perform the required hypothesis test.
Part (c): Compare your results in parts (a) and (b).
Part (d): Explain what principle is being illustrated.
In each of Exercises 12.24-12.33, apply the chi-square goodness-of-fit test, using either the critical-value approach or thevalue approach, to perform the required hypothesis test.
An American roulette wheel contains red numbers, black numbers, and green numbers. The following table shows the frequency with which the ball landed on each color in trials.
At the significance level, do the data suggest that the wheel is out of balance?
A chi-square independence test is to be conducted to decide whether an association exists between two variables of a population. One variable has six possible values, and the other variable has four. What is the degrees of freedom for the statistic?
Are the observed frequencies variables? What about the expected frequencies? Explain your answers.
Table 12.4 on page 486 showed the calculated sums of the observed frequencies, the expected frequencies, and their differences. Strictly speaking, those sums are not needed. However, they serve as a check for computational errors.
a) In general, what common value should the sum of the observer frequencies and the sum of the expected frequencies equal? Ex plain your answer.
b) Fill in the blank. The sum of the differences between each observed and expected frequency should equal
c) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies does not equal the sample size, what do you conclude?
d) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies equals the sample size, can you conclude that you made no error in calculating the expected frequencies? Explain your answer.
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