Chapter 12: Q. 12.36 (page 499)
Find the type of table that is used to group bivariate data.
Ans: A contingency table or two-way table is the name of the table used to group bivariate data.
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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.
Identify three techniques that can be tried as a remedy when one or more of the expected-frequency assumptions for a chi-square independence test are violated.
In each of the given Exercises, we have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x, and y, of a population. For each exercise, perform the following tasks.
a. Find the expected frequencies. Note: You will first need to compute the row totals, column totals, and grand total.
b. Determine the value of the chi-square statistic.
c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.
Scoliosis is a condition involving curvature of the spine. In a study by A. Nachemson and L. Peterson, reported in the Journal of Bone and Joing Surgery, girls aged to years were followed to determine the effects of observation only (patients), an underarm plastic brace (patients), and nighttime surface electrical stimulation ( patients). A treatment was deemed to have failed if the curvature of the spine increased by 6 on two successive examinations. The following table summarizes the results obtained by the researchers.
At the significance level, do the data provide sufficient evidence to conclude that a difference in failure rate exists among the three types of treatments?
In each of Exercises 12.11-12.16, we have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fir text and the sample size. In each case, decide whether Assumptions 1 and 2 for using that text are satisfied.
Sample size : n= 50.
Relative frequencies: 0.22 , 0.21 , 0.25 , 0.30 , 0.02.
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