Define the sets A₁ = {x : −∞ < x ≤ 0}, A_i = {x : i − 2 < x ≤ i − 1}, i = 2, . . . , 7, and A₈ = {x : 6 < x < ∞}. A certain hypothesis assigns probabilities p_i0 to these sets A_i in accordance with

This hypothesis (concerning the multinomial pdf with k = 8) is to be tested, at the 5% level of significance, by a chi-square test. If the observed frequencies of the sets A_i, i = 1, 2, . . . , 8, are, respectively, 60, 96, 140, 210, 172, 160, 88, and 74, would H₀ be accepted at the (approximate) 5% level of significance?

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Pio 1 = - 1₁, 2√/ ZE XP [- exp (x - 3)²] 2(4) dx, i=1,2,...,7,8.