6.61. A random sample of size 40 has y = 120. The Pvalue for testing Hq: p. = 100 against/7„: p, * 100 is P = 0.057. Explain what is incorrect about each of the following interpretations of this P-value, and provide a proper interpretation.

(a) The probability that the null hypothesis is correct equals 0.057.

(b) The probability that y = 120 if Hq is true equals 0.057.

(c) If in fact p.* 100, the probability equals 0.057 thatthe data would be at least as contradictory to Hq as the observed data.

(d) The probability of Type I error equals 0.057.

(e) We can accept Hq at the a - 0.05 level.

(f) We can reject Hq at the a = 0.05 level.