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 = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.5 inches, with estimated standard deviation s = 3.0 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than u = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 19 in; H,: µ > 19 in Ho: H < 19 in; H,: µ = 19 in O Ho: H = 19 in; H,: µ < 19 in O Ho: H = 19 in; H,: µ + 19 in O Ho: H > 19 in; H,: µ = 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 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 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. O P-value > 0.250 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010
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 = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.5 inches, with estimated standard deviation s = 3.0 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than u = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 19 in; H,: µ > 19 in Ho: H < 19 in; H,: µ = 19 in O Ho: H = 19 in; H,: µ < 19 in O Ho: H = 19 in; H,: µ + 19 in O Ho: H > 19 in; H,: µ = 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 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 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. O P-value > 0.250 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010
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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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 u = 19
inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.5 inches, with estimated standard deviation s = 3.0 inches. Do these data indicate that
the average length of a trout caught in Pyramid Lake is less than u = 19 inches? Use a = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: H = 19 in; H,: µ > 19 in
Ho: H < 19 in; H,: µ = 19 in
O Ho: H = 19 in; H,: µ < 19 in
O Ho: H = 19 in; H,: µ + 19 in
O Ho: H > 19 in; H,: µ = 19 in
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
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 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.
O P-value > 0.250
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
O P-value < 0.010
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