Answer Happy

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 2.7 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ = 19 inches? Use a = 0.05. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: μ = 19 in; H₁: μ > 19 in O Ho: μ > 19 in; H₁: μ = 19 in Ho: μ< 19 in; H₁: μ = 19 in Ho: μ = 19 in; H₁: μ< 19 in O Ho: μ = 19 in; H₁: μ = 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and σ is known. The Student's t, since the sample size is large and σ is unknown. O The standard normal, since the sample size is large and o known. O The standard normal, since the sample size is large and σ is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.010 0.0010 < P-value < 0.010 O 0.250 < P-value < 0.0010 0.125 < P-value < 0.250 OP-value < 0.125
Sketch the sampling distribution and show the area corresponding to the P-value. 0 -4 e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches. O There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches. -2 d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 0 2 AO -2 0 2