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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 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= 3.1 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? 10.05 State the null and alternate hypotheses. Ho: 19 in; H₁: μ = 19 in Ho: M 19 in; H₁: > 19 in Ho: > 19 in; H₁: μ = 19 in Ho: M 19 in; H₁: # 19 in O Ho: = 19 in; H₁: μ< 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and is known. O The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and a is known. O The standard normal, since the sample size is large and o is unknown. X What is the value of the sample test statistic? (Round your answer to three decimal places.) 4-0.921 (c) Estimate the P-value. OP-value > 0.010 0.0010 < P-value < 0.010 0.250 < P-value < 0.0010 O 0.125 P-value < 0.250 P-value < 0.125

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= 3.1 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? 10.05 State the null and alternate hypotheses. Ho: 19 in; H₁: μ = 19 in Ho: M 19 in; H₁: > 19 in Ho: > 19 in; H₁: μ = 19 in Ho: M 19 in; H₁: # 19 in O Ho: = 19 in; H₁: μ< 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and is known. O The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and a is known. O The standard normal, since the sample size is large and o is unknown. X What is the value of the sample test statistic? (Round your answer to three decimal places.) 4-0.921 (c) Estimate the P-value. OP-value > 0.010 0.0010 < P-value < 0.010 0.250 < P-value < 0.0010 O 0.125 P-value < 0.250 P-value < 0.125

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 22SGR
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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 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 = 3.1 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? 1 0.05 State the null and alternate hypotheses. Ho: μ< 19 in; H₁: µ = 19 in H₁: μ = 19 in; H₁: > 19 in Ho: μ> 19 in; H₁: μ = 19 in Ho: μ = 19 in; H₁: μ ‡ 19 in Ho: μ = 19 in; H₁: μ< 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and o is known. The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and o is known. The standard normal, since the sample size is large and o is unknown. (c) What is the value of the sample test statistic? (Round your answer to three decimal places.) 4 -0.921 Estimate the P-value. P-value > 0.010 0.0010 < P-value < 0.010 0.250 < P-value < 0.0010 0.125 < P-value < 0.250 P-value < 0.125 • Ο Ο Ο
Transcribed Image Text: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 = 3.1 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? 1 0.05 State the null and alternate hypotheses. Ho: μ< 19 in; H₁: µ = 19 in H₁: μ = 19 in; H₁: > 19 in Ho: μ> 19 in; H₁: μ = 19 in Ho: μ = 19 in; H₁: μ ‡ 19 in Ho: μ = 19 in; H₁: μ< 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and o is known. The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and o is known. The standard normal, since the sample size is large and o is unknown. (c) What is the value of the sample test statistic? (Round your answer to three decimal places.) 4 -0.921 Estimate the P-value. P-value > 0.010 0.0010 < P-value < 0.010 0.250 < P-value < 0.0010 0.125 < P-value < 0.250 P-value < 0.125 • Ο Ο Ο
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