Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fish caught fishing from the shore, and let row A represent hours per fish caught using a boat. The following data are paired by month from October through April. Oct Nov Dec Jan Feb March April B: Shore 2.0 1.6 1.5 3.2 3.9 3.6 3.3 A: Boat 1.9 2.0 1.7 2.2 3.3 3.0 3.8 Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: ?d = 0; H1: ?d ≠ 0; two-tailedHo: ?d = 0; H1: ?d < 0; left-tailed Ho: ?d ≠ 0; H1: ?d = 0; two-tailedHo: ?d = 0; H1: ?d > 0; right-tailed (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately normal distribution.The standard normal. We assume that d has an approximately normal distribution. The standard normal. We assume that d has an approximately uniform distribution.The Student's t. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Use 3 decimal places.) (c) Find (or estimate) the P-value. (Use degrees of freedom equal to the smaller of n1 − 1 and n2 − 1. Use 4 decimal places.) 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 ?? At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) State your conclusion in the context of the application. Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing. Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.

Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fish caught fishing from the shore, and let row A represent hours per fish caught using a boat. The following data are paired by month from October through April. Oct Nov Dec Jan Feb March April B: Shore 2.0 1.6 1.5 3.2 3.9 3.6 3.3 A: Boat 1.9 2.0 1.7 2.2 3.3 3.0 3.8 Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: ?d = 0; H1: ?d ≠ 0; two-tailedHo: ?d = 0; H1: ?d < 0; left-tailed Ho: ?d ≠ 0; H1: ?d = 0; two-tailedHo: ?d = 0; H1: ?d > 0; right-tailed (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately normal distribution.The standard normal. We assume that d has an approximately normal distribution. The standard normal. We assume that d has an approximately uniform distribution.The Student's t. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Use 3 decimal places.) (c) Find (or estimate) the P-value. (Use degrees of freedom equal to the smaller of n1 − 1 and n2 − 1. Use 4 decimal places.) 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 ?? At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) State your conclusion in the context of the application. Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing. Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 26PFA

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Related questions

Question

	Oct	Nov	Dec	Jan	Feb	March	April
B: Shore	2.0	1.6	1.5	3.2	3.9	3.6	3.3
A: Boat	1.9	2.0	1.7	2.2	3.3	3.0	3.8

Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore.

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H_o: ?_d = 0; H₁: ?_d ≠ 0; two-tailedH_o: ?_d = 0; H₁: ?_d < 0; left-tailed H_o: ?_d ≠ 0; H₁: ?_d = 0; two-tailedH_o: ?_d = 0; H₁: ?_d > 0; right-tailed

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that d has an approximately normal distribution.The standard normal. We assume that d has an approximately normal distribution. The standard normal. We assume that d has an approximately uniform distribution.The Student's t. We assume that d has an approximately uniform distribution.

What is the value of the sample test statistic? (Use 3 decimal places.)

(c) Find (or estimate) the P-value. (Use degrees of freedom equal to the smaller of n₁− 1 and n₂ − 1. Use 4 decimal places.)

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 ??

At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

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

Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing. Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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