Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows. 6.19 6.26 5.84 6.12 7.31 7.18 7.06 5.79 6.24 5.91 6.14 Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.302. Another random sample of years for a second plot gave the following annual wheat production (in pounds). 6.75 6.05 7.17 6.33 7.22 5.58 5.47 5.86 Use a calculator to verify that the sample variance for this plot is s2 ≈ 0.467. Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance. (a) What is the level of significance? State the null and alternate hypotheses. Ho: ?12 = ?22; H1: ?12 > ?22Ho: ?12 > ?22; H1: ?12 = ?22 Ho: ?22 = ?12; H1: ?22 > ?12Ho: ?12 = ?22; H1: ?12 ≠ ?22 (b) Find the value of the sample F statistic. (Use 2 decimal places.) What are the degrees of freedom? dfN dfD What assumptions are you making about the original distribution? The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent normal distributions. We have random samples from each population. The populations follow independent normal distributions.The populations follow independent chi-square distributions. We have random samples from each population. (c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.) p-value > 0.2000.100 < p-value < 0.200 0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002

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 3CYU

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Question

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

6.19	6.26	5.84	6.12	7.31	7.18
7.06	5.79	6.24	5.91	6.14

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.302.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

6.75

6.05

7.17

6.33

7.22

5.58

5.47

5.86

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.467.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: ?₁² = ?₂²; H₁: ?₁² > ?₂²H_o: ?₁² > ?₂²; H₁: ?₁² = ?₂² H_o: ?₂² = ?₁²; H₁: ?₂² > ?₁²H_o: ?₁² = ?₂²; H₁: ?₁² ≠ ?₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

df_N
df_D

What assumptions are you making about the original distribution?

The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent normal distributions. We have random samples from each population. The populations follow independent normal distributions.The populations follow independent chi-square distributions. We have random samples from each population.

p-value > 0.2000.100 < p-value < 0.200 0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002

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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