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
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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Question
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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