(Solved): A-E Pyramid Lake is on the Paiute Indian Reservation in Nevada, The Inke is famous for cutthroat tro ...

Pyramid Lake is on the Paiute Indian Reservation in Nevada, The Inke is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in. Pyramid Lake is \( \mu=19 \) inches. However, a survey reported that of a random sample of si fish caught, the mean length was \( x=18,6 \) inches, with entimated standard deviation \( 5=3.1 \) incher, Do these dato indicate that the average length of a trout ceught in Pyramid Lake is less than \( \mu=19 \) inches? Use \( \alpha=0.05 \). (a) What is the level of significance? State the null and alternatelhypotheses. \[ \begin{array}{l} H_{0} ; \mu=19 \text { in; } H_{1}: \mu \neq 19 \text { in } \\ H_{0} ; \mu<19 \text { in; } H_{1}: \mu=19 \text { in } \\ H_{0}: \mu=19 \text { in; } H_{1}: \mu<19 \text { in } \\ H_{0}: \mu=19 \text { in; } H_{1}: \mu>19 \text { in } \\ H_{0}: \mu>19 \text { in; } H_{1}: \mu=19 \text { in } \end{array} \] (b) What sampling distribution Will you use? Explain the rationale for yout choice of sampling distribution. The standard normal, since the sample size is large and is is known. The Student's t, since the sample size is large and in is known. The Student's t, rince the sample size is large and o is unknown, The standard normal, since the sample size is large and o is uriknown. What is the yalue of the sample test statistic? (Round your answer to three decimal places.) \( 0.0010