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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 = 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= 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ho: = 19 in; H₁: μ # 19 in > 19 in; H₁: μ = 19 in O Ho: Ho: < 19 in; H₁: μ = 19 in O Ho: = 19 in; H₁: μ> 19 in OH: = 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 o is unknown. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and a is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. OP-value > 0.010 O 0.0010 < P-value < 0.010 O 0.250 < P-value < 0.0010 O 0.125 < P-value < 0.250 O P-value < 0.125 Sketch the sampling distribution and show the area corresponding to the P-value. ^ 4

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 = 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= 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ho: = 19 in; H₁: μ # 19 in > 19 in; H₁: μ = 19 in O Ho: Ho: < 19 in; H₁: μ = 19 in O Ho: = 19 in; H₁: μ> 19 in OH: = 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 o is unknown. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and a is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. OP-value > 0.010 O 0.0010 < P-value < 0.010 O 0.250 < P-value < 0.0010 O 0.125 < P-value < 0.250 O P-value < 0.125 Sketch the sampling distribution and show the area corresponding to the P-value. ^ 4

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Sketch the sampling distribution and show the area corresponding to the P-value. O O -4 -2 -2 0 2 2 H i 4 -2 C 2 12 io (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. 7 -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 a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 0 2 4 4 i
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. O O -4 -2 -2 0 2 2 H i 4 -2 C 2 12 io (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. 7 -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 a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 0 2 4 4 i
= 19 inches. 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 u 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 = 3.3 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. = (a) What is the level of significance? State the null and alternate hypotheses. O 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 O 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 o is unknown. O The standard normal, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. OP-value > 0.010 O 0.0010 < P-value < 0.010 O 0.250 < P-value < 0.0010 0.125 < P-value < 0.250 O P-value < 0.125 Sketch the sampling distribution and show the area corresponding to the P-value.
Transcribed Image Text:= 19 inches. 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 u 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 = 3.3 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. = (a) What is the level of significance? State the null and alternate hypotheses. O 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 O 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 o is unknown. O The standard normal, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. OP-value > 0.010 O 0.0010 < P-value < 0.010 O 0.250 < P-value < 0.0010 0.125 < P-value < 0.250 O P-value < 0.125 Sketch the sampling distribution and show the area corresponding to the P-value.
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