A multinomial experiment produced the following results (Use Table 3): 
Category  1  2  3  4  5 
Frequency  62  58  65  70  70 
a. 
Choose the appropriate alternative hypothesis to test if the population proportions differ. 


b. 
Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.) 
χ^{2}_{df} 
c. 
Specify the decision rule at the 10% significance level. (Round your answer to 3 decimal places.) 
Reject H_{0} if x^{2}_{df} > 
d. 
Can we conclude at the 10% significance level that the population proportions are not equal? 


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