How does the difference between f, and f, influence the outcome of a chi-square test? The larger the difference, the larger the value of chi-square and the lower the likelihood of rejecting the null hypothesis. The larger the difference, the larger the value of chi-square and the greater the likelihood of rejecting the null hypothesis. The larger the difference, the smaller the value of chi-square and the lower the likelihood of rejecting the null hypothesis. The larger the difference, the smaller the value of chi-square and the greater the likelihood of rejecting the null hypothesis.

The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the α=0.1 level of significance.     Category 1 Category 2 Category 3   Failures 32 51 57 Successes 39 54 73 State the hypotheses. Choose the correct answer below.     A. H0​: The categories of the variable and success and failure are independent. H1​: The categories of the variable and success and failure are dependent.   B. H0​: The categories of the variable and success and failure are dependent. H1​: The categories of the variable and success and failure are independent.   C. H0​: p1=p2=p3 H1​: At least one of the proportions is different from the others.   D. H0​: μ1=E1 and μ2=E2 and μ3=E3 H1​: At least one mean is different from what is expected. What is the​ P-value?   nothing ​(Round to three decimal places as​ needed.) What conclusion can be​…

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It has recently been claimed that 25% of adults consider spring to be their favorite season of the year. A researcher is skeptical of this claim and believes this percentage is too low.  She surveys a random of 1,000 adults and finds that 390 of these adults consider spring to be their favorite season of the year.  As she prepares to conduct a hypothesis test, the researcher writes out her alternative hypothesis as “p < 0.25.”  What is wrong with this?   The alternative hypothesis should be “p > 0.39.” The alternative hypothesis should be “p < 0.39.” The alternative hypothesis should be “p > 0.25.” The alternative hypothesis should be “p = 0.25.” Nothing is wrong with the given alternative hypothesis.