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6. [-14.08 Points] BBUNDERSTAT12 8.2.014.MI.S. ASK YOUR TEACHER Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lIke is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ,u = 19 inches. However, a survey reported that of a rIndom sImpIe of 45 sh caught, the mean length was i = 10.4 inches, with estimated standard deviation 5 = 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ,u = 19 inches? Use cx = 0.05. l uses T (a) What is the level of significance? : State the null and alternate hypotheses. O Hu:u19in;H1:j.t=19in O Hozu=19in;H.I:_u>19in O Hu:u=19in;H.|:,u19in (a) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 0 The Student's t. since the sample size is large and 0' is unknown. 0 The standard normal, since the sample size is large and ' is unknown. 0 The Student's t. since the sample size is large and 0' is known. 0 The standard normal, since the sample size is large and (r is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) : (c) Estimate the Pvalue. O Pvalue > 0.0010 0 0.500