Question

The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to take a random sample of 400 seeds and conduct a two-sided test with the null hypothesis H0: p = 0.8 using ? = 0.05. They determine that the power of this test against the alternative p = 0.75 is 0.69. Interpret the power of this test. (b) Describe two ways that the company can increase the power of the test. What is the disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate (0.726, 0.809). Use this confidence interval to determine whether the test described in Part (a) would reject or fail to reject the null hypothesis. Explain your reasoning.

          The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species.

(a) Suppose the company plans to take a random sample of 400 seeds and conduct a two-sided test with the null hypothesis H0: p = 0.8 using ? = 0.05. They determine that the power of this test against the alternative p = 0.75 is 0.69. Interpret the power of this test.

(b) Describe two ways that the company can increase the power of the test. What is the disadvantage of each of these ways?

(c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate (0.726, 0.809). Use this confidence interval to determine whether the test described in Part (a) would reject or fail to reject the null hypothesis. Explain your reasoning.

The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species.

(a) Suppose the company plans to take a random sample of 400 seeds and conduct a two-sided test with the null hypothesis H0: p = 0.8 using ? = 0.05. They determine that the power of this test against the alternative p = 0.75 is 0.69. Interpret the power of this test.

(b) Describe two ways that the company can increase the power of the test. What is the disadvantage of each of these ways?

(c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate (0.726, 0.809). Use this confidence interval to determine whether the test described in Part (a) would reject or fail to reject the null hypothesis. Explain your reasoning.

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