Sample Size E. coli Prevalence Organic 260 3 Conventional 510 20 Is there a significant difference in the proportion of E. coli in organic vs. conventionally grown produce? Test at a = 0.10. (Let d = Organic - Conventional.) (a) Formulate the hypotheses. $H_0: p_1 - p_2 = 0$ $H_a: p_1 - p_2 \neq 0$ (b) What is the value of the test statistic? (Round your answer to three decimal places.) (c) What is the p-value? (Round your answer to three decimal places.) p-value = (d) What is your conclusion? Reject $H_0$. We can conclude that there is a significant difference in the proportion of E. coli in organic vs. conventional produce. Reject $H_0$. We cannot conclude that there is a significant difference in the proportion of E. coli in organic vs. conventional produce. Do not reject $H_0$. We cannot conclude that there is a significant difference in the proportion of E. coli in organic vs. conventional produce. Do not reject $H_0$. We can conclude that there is a significant difference in the proportion of E. coli in organic vs. conventional produce.
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$p_1 = \frac{3}{260} \approx 0.0115$ $p_2 = \frac{20}{510} \approx 0.0392$ Show more…
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A comparative study of organic and conventionally grown produce was conducted to check for the presence of E.coli. The results are summarized below. We want to determine if a significant difference exists in the proportion of E. coli in organic versus conventionally grown produce. Sample Size E.Coli Prevalence Organic 200 7 Conventional 500 17 Test the hypothesis in question 7a with alpha = .05. Do you accept or reject the null hypothesis of Question 7a? Accept Reject
Cheng Z.
A) In a representative sample of 736 coffee growers from Country X, 351 growers were certified to sell organic coffee while 72 growers were transitioning to become organic certified. In Country Y, 61% of coffee growers are organic certified. Is there evidence to indicate that fewer than 61% of the coffee growers in Country X are either organic certified or transitioning to become organic certified? State your conclusion so that there is only a 10% chance of making a Type I error. What are the hypotheses for this test? A. H0: p=0.61 Ha: p≠0.61 B. H0: p=0.61 Ha: p<0.61 C. H0: p≥0.61 Ha: p<0.61 D. H0: p=0.61 Ha: p>0.61 E. H0: p<0.61 Ha: p=0.61 F. H0: p>0.61 Ha: p≤0.61 Calculate the value of the z-statistic for this test. Z = ----------- (Round to two decimal places as needed.) Calculate the p-value for this test. p-value = ---------- (Round to three decimal places as needed.) What is the conclusion of the test? (Reject OR Do not reject?) The null hypothesis because the p-value is (Less than OR Greater than) the probability of making a Type I error. Therefore, there is (Sufficient OR Insufficient) evidence to indicate that fewer than 61% of the coffee growers in Country X are either organic certified or transitioning to become organic certified. In a test of the hypothesis H0: μ=10 versus Ha: μ≠10, a sample of n=50 observations possessed mean x=10.7 and standard deviation s=2.6. Find and interpret the p-value for this test. Interpret the result. Choose the correct answer below. A. There is insufficient evidence to reject H0 for α = 0.15. B. There is sufficient evidence to reject H0 for α<0.06. C. There is sufficient evidence to reject H0 for α>0.06.
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A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data. 1.19 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.13 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.91 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.72 1.17 1.57 2.62 1.66 2.05 The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.480, 1.613, and 0.294, respectively. Does this data suggest that the true average percentage of organic matter in such soil is something other than 3%? Carry out a test of the appropriate hypotheses at significance level 0.10. [Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.] State the appropriate hypotheses. H0: μ = 3 Ha: μ ≠ 3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = -1.769 P-value = 0.083 What can you conclude? Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Would your conclusion be different if α = 0.05 had been used? Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%.
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