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 46 fish caught, the mean length was x = 18.6 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 ? = 19 inches? Use ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: ? = 19 in; H1: ? ≠ 19 inH0: ? = 19 in; H1: ? > 19 in H0: ? < 19 in; H1: ? = 19 inH0: ? > 19 in; H1: ? = 19 inH0: ? = 19 in; H1: ? < 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and ? is known.The standard normal, since the sample size is large and ? is known. The Student's t, since the sample size is large and ? is unknown.The standard normal, 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. P-value > 0.0100.0010 < P-value < 0.010 0.250 < P-value < 0.00100.125 < P-value < 0.250P-value < 0.125 Sketch the sampling distribution and show the area corresponding to the P-value. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 0.82 and 4 is shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.82 as well as the area under the curve between 0.82 and 4 are both shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −0.82 and 4 is shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.82 is shaded. (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 ?? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.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. There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.

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 46 fish caught, the mean length was x = 18.6 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 ? = 19 inches? Use ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: ? = 19 in; H1: ? ≠ 19 inH0: ? = 19 in; H1: ? > 19 in H0: ? < 19 in; H1: ? = 19 inH0: ? > 19 in; H1: ? = 19 inH0: ? = 19 in; H1: ? < 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and ? is known.The standard normal, since the sample size is large and ? is known. The Student's t, since the sample size is large and ? is unknown.The standard normal, 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. P-value > 0.0100.0010 < P-value < 0.010 0.250 < P-value < 0.00100.125 < P-value < 0.250P-value < 0.125 Sketch the sampling distribution and show the area corresponding to the P-value. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 0.82 and 4 is shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.82 as well as the area under the curve between 0.82 and 4 are both shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −0.82 and 4 is shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.82 is shaded. (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 ?? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.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. There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.

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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Related questions

Question

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀: ? = 19 in; H₁: ? ≠ 19 inH₀: ? = 19 in; H₁: ? > 19 in H₀: ? < 19 in; H₁: ? = 19 inH₀: ? > 19 in; H₁: ? = 19 inH₀: ? = 19 in; H₁: ? < 19 in

(b)

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

The Student's t, since the sample size is large and ? is known.The standard normal, since the sample size is large and ? is known. The Student's t, since the sample size is large and ? is unknown.The standard normal, 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.

P-value > 0.0100.0010 < P-value < 0.010 0.250 < P-value < 0.00100.125 < P-value < 0.250P-value < 0.125

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

A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 0.82 and 4 is shaded.

(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 ??

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

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