Questions A and B. Please! **Problem Context:**Pyramid Lake is located on the Paiute Indian Reservation in Nevada and is known for its cutthroat trout population. It is believed that the average length of trout caught in Pyramid Lake is $ \mu = 19 $ inches. A friend provides data from a survey where a random sample of 46 fish was caught, showing a mean length of $ \bar{x} = 18.4 $ inches with an estimated standard deviation of $ s = 3.3 $ inches. The question is whether these data indicate that the average length of a trout in Pyramid Lake is less than $ \mu = 19 $ inches, using a significance level of $ \alpha = 0.05 $.**Part (a):****What is the level of significance?**- The level of significance is $ \alpha = 0.05 $.**State the null and alternate hypotheses:**- Null Hypothesis ($ H_0 $): $ \mu = 19 \, \text{inches} $- Alternate Hypothesis ($ H_1 $): $ \mu < 19 \, \text{inches} $The correct selection is:- $ H_0: \mu = 19 \, \text{in}; \, H_1: \mu < 19 \, \text{in} $**Part (b):****What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.**The choice is:- The Student’s $ t $, since the sample size is large and $ \sigma $ (population standard deviation) is unknown.This is because the sample size is relatively large (46), which justifies using the Student’s $ t $-distribution, especially when the population standard deviation is unknown.**Additional Information:**The calculation of the test statistic would follow, asking for the value of the sample test statistic rounded to three decimal places. However, the specific result is not included in the provided image or text description.

Name: Questions A and B. Please! **Problem Context:**Pyramid Lake is located
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Description: Questions A and B. Please! **Problem Context:**Pyramid Lake is located on the Paiute Indian Reservation in Nevada and is known for its cutthroat trout population. It is believed that the average length of trout caught in Pyramid Lake is \( \mu = 19 \

Sample size (n) = 46 Sample mean (x̅) = 18.4 inches Sample standard deviation (s) = 3.3 inchesa) The level of significance (α) = 0.05 The hypotheses are as follow: H0: µ = 19 inches H1: µ < 19 inchesb) The sample size is large and population standard deviation (σ) is unknown, therefore, the student’s t distribution will be used. The value of the test statistic can be obtained as:

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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 u = 19 inches. However, a survey reported that cof a random sample of 46 fish caught, the mean length was x = 18.4 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 u = 19 inches? Use a = 0.05. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O H,; u > 19 in; H,:# = 19 in O H,i u = 19 in; H,i u # 19 in O H,i u < 19 in; H, u = 19 in O H,i = 19 in; H, 1 u > 19 in O H,i u 19 in; H, u < 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and e is known. The Student's r, since the sample size is large and e is known. • The Student's t, since the sample size is large and a is unknown. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three 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 cof a random sample of 46 fish caught, the mean length was x = 18.4 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 u = 19 inches? Use a = 0.05. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O H,; u > 19 in; H,:# = 19 in O H,i u = 19 in; H,i u # 19 in O H,i u < 19 in; H, u = 19 in O H,i = 19 in; H, 1 u > 19 in O H,i u 19 in; H, u < 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and e is known. The Student's r, since the sample size is large and e is known. • The Student's t, since the sample size is large and a is unknown. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.)

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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Questions A and B. Please!

**Problem Context:**

Pyramid Lake is located on the Paiute Indian Reservation in Nevada and is known for its cutthroat trout population. It is believed that the average length of trout caught in Pyramid Lake is $ \mu = 19 $ inches. A friend provides data from a survey where a random sample of 46 fish was caught, showing a mean length of $ \bar{x} = 18.4 $ inches with an estimated standard deviation of $ s = 3.3 $ inches. The question is whether these data indicate that the average length of a trout in Pyramid Lake is less than $ \mu = 19 $ inches, using a significance level of $ \alpha = 0.05 $.

**Part (a):**

**What is the level of significance?**

- The level of significance is $ \alpha = 0.05 $.

**State the null and alternate hypotheses:**

- Null Hypothesis ($ H_0 $): $ \mu = 19 \, \text{inches} $
- Alternate Hypothesis ($ H_1 $): $ \mu < 19 \, \text{inches} $

The correct selection is:

- $ H_0: \mu = 19 \, \text{in}; \, H_1: \mu < 19 \, \text{in} $

**Part (b):**

**What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.**

The choice is:

- The Student’s $ t $, since the sample size is large and $ \sigma $ (population standard deviation) is unknown.

This is because the sample size is relatively large (46), which justifies using the Student’s $ t $-distribution, especially when the population standard deviation is unknown.

**Additional Information:**

The calculation of the test statistic would follow, asking for the value of the sample test statistic rounded to three decimal places. However, the specific result is not included in the provided image or text description.

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