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 = 18.5 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 ? = 19 inches? Use ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. What is the value of the sample test statistic? (c) Estimate the P-value. 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 ?? (e) Interpret your conclusion in the context of the application.
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 = 18.5 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 ? = 19 inches? Use ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. What is the value of the sample test statistic? (c) Estimate the P-value. 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 ?? (e) Interpret your conclusion in the context of the application.
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 = 18.5 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 ? = 19 inches? Use ? = 0.05.
(a)
What is the level of significance?
State the null and alternate hypotheses.
(b)
What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
What is the value of the sample test statistic?
(c)
Estimate the P-value.
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 ??
(e)
Interpret your conclusion in the context of the application.
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