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 = 3.5 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. (a)What is the level of significance? = State the null and alternate hypotheses. A-H0: ? = 19 in; H1: ? ≠ 19 in B-H0: ? < 19 in; H1: ? = 19 in C-H0: ? = 19 in; H1: ? < 19 in D-H0: ? = 19 in; H1: ? > 19 in E-H0: ? > 19 in; H1: ? = 19 in (b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. A-The Student's t, since the sample size is large and ? is known. B-The standard normal, since the sample size is large and ? is known. C-The standard normal, since the sample size is large and ? is unknown. D-The Student's t, since the sample size is large and ? is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) =_ (c)Estimate the P-value. A-P-value > 0.010 B-0.0010 < P-value < 0.010 C-0.250 < P-value < 0.0010 D-0.125 < P-value < 0.250 E-P-value < 0.125

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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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 = 3.5 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05.

(a)What is the level of significance?

=__

State the null and alternate hypotheses.

A-H₀: ? = 19 in; H₁: ? ≠ 19 in

B-H₀: ? < 19 in; H₁: ? = 19 in

C-H₀: ? = 19 in; H₁: ? < 19 in

D-H₀: ? = 19 in; H₁: ? > 19 in

E-H₀: ? > 19 in; H₁: ? = 19 in

(b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

A-The Student's t, since the sample size is large and ? is known.

B-The standard normal, since the sample size is large and ? is known.

C-The standard normal, since the sample size is large and ? is unknown.

D-The Student's t, since the sample size is large and ? is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)
=___

(c)Estimate the P-value.

A-P-value > 0.010

B-0.0010 < P-value < 0.010

C-0.250 < P-value < 0.0010

D-0.125 < P-value < 0.250

E-P-value < 0.125

Sketch the sampling distribution and show the area corresponding to the P-value.

(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-At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

B-At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

C-At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

D-At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)Interpret your conclusion in the context of the application.

A-There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.

B-There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.

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