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 51 fish caught, the mean length was x = 18.7 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 H = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: u > 19 in; H1: µ = 19 in O Ho: H = 19 in; H1: u < 19 in O Họ: H = 19 in; H1: H + 19 in O Họ: H < 19 in; H1: H = 19 in O Họ: H = 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. 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) Find the P-value. (Round your answer to four decimal places.)
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 51 fish caught, the mean length was x = 18.7 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 H = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: u > 19 in; H1: µ = 19 in O Ho: H = 19 in; H1: u < 19 in O Họ: H = 19 in; H1: H + 19 in O Họ: H < 19 in; H1: H = 19 in O Họ: H = 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. 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) Find the P-value. (Round your answer to four decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![**Title: Statistical Analysis of Trout Length in Pyramid Lake**
Pyramid Lake is on the Paiute Indian Reservation in Nevada, known for cutthroat trout. A survey reported that out of a random sample of 51 fish caught, the mean length was \( \bar{x} = 18.7 \) inches, with an estimated standard deviation \( s = 3.1 \) inches. We aim to determine if these data indicate that the average length of a trout caught in Pyramid Lake is less than \( \mu = 19 \) inches. We will use a significance level of \( \alpha = 0.05 \).
---
**(a) What is the level of significance?**
\[ \alpha = \]
**State the null and alternate hypotheses.**
- \( H_0: \mu = 19 \text{ in}; \quad H_1: \mu < 19 \text{ in} \)
- \( \circ \quad H_0: \mu \neq 19 \text{ in}; \quad H_1: \mu < 19 \text{ in} \)
- \( \circ \quad H_0: \mu > 19 \text{ in}; \quad H_1: \mu = 19 \text{ in} \)
- \( \circ \quad H_0: \mu < 19 \text{ in}; \quad H_1: \mu = 19 \text{ in} \)
- \( \circ \quad H_0: \mu = 19 \text{ in}; \quad H_1: \mu > 19 \text{ in} \)
---
**(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.**
- \( \bullet \quad \text{The Student's } t, \text{ since the sample size is large and } \sigma \text{ is unknown.} \)
- \( \circ \quad \text{The standard normal, since the sample size is large and } \sigma \text{ is unknown.} \)
- \( \circ \quad \text{The Student's } t, \text{ since the sample size is large and } \sigma \text{ is known.} \)
- \( \circ \quad \text{The standard normal, since the sample size is large and } \sigma \text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F263d6acc-03b4-45b5-8ce2-d676aa9ac999%2F0b9de202-8dcb-47ef-a514-ae8cac8e6563%2Fp6ezlfj_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Statistical Analysis of Trout Length in Pyramid Lake**
Pyramid Lake is on the Paiute Indian Reservation in Nevada, known for cutthroat trout. A survey reported that out of a random sample of 51 fish caught, the mean length was \( \bar{x} = 18.7 \) inches, with an estimated standard deviation \( s = 3.1 \) inches. We aim to determine if these data indicate that the average length of a trout caught in Pyramid Lake is less than \( \mu = 19 \) inches. We will use a significance level of \( \alpha = 0.05 \).
---
**(a) What is the level of significance?**
\[ \alpha = \]
**State the null and alternate hypotheses.**
- \( H_0: \mu = 19 \text{ in}; \quad H_1: \mu < 19 \text{ in} \)
- \( \circ \quad H_0: \mu \neq 19 \text{ in}; \quad H_1: \mu < 19 \text{ in} \)
- \( \circ \quad H_0: \mu > 19 \text{ in}; \quad H_1: \mu = 19 \text{ in} \)
- \( \circ \quad H_0: \mu < 19 \text{ in}; \quad H_1: \mu = 19 \text{ in} \)
- \( \circ \quad H_0: \mu = 19 \text{ in}; \quad H_1: \mu > 19 \text{ in} \)
---
**(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.**
- \( \bullet \quad \text{The Student's } t, \text{ since the sample size is large and } \sigma \text{ is unknown.} \)
- \( \circ \quad \text{The standard normal, since the sample size is large and } \sigma \text{ is unknown.} \)
- \( \circ \quad \text{The Student's } t, \text{ since the sample size is large and } \sigma \text{ is known.} \)
- \( \circ \quad \text{The standard normal, since the sample size is large and } \sigma \text{
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