Consider the following hypotheses: H0: μ ≤ 73.0 HA: μ > 73.0 A sample of 51 observations yields a sample mean of 74.3. Assume that the sample is drawn from a normal population with a population standard deviation of 3.7. (You may find it useful to reference the appropriate table: z table or t table) a-1. Find the p-value. multiple choice 1 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 a-2. What is the conclusion if α = 0.01? multiple choice 2 Do not reject H0 since the p-value is smaller than α. Do not reject H0 since the p-value is greater than α. Reject H0 since the p-value is smaller than α. Reject H0 since the p-value is greater than α. a-3. Interpret the results at α = 0.01. multiple choice 3 We cannot conclude that the sample mean is greater than 73. We conclude that the sample mean is greater than 73. We cannot conclude that the population mean is greater than 73. We conclude that the population mean is greater than 73. b-1. Calculate the p-value if the above sample mean was based on a sample of 118 observations. multiple choice 4 p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10 b-2. What is the conclusion if α = 0.01? multiple choice 5 Reject H0 since the p-value is smaller than α. Reject H0 since the p-value is greater than α. Do not reject H0 since the p-value is smaller than α. Do not reject H0 since the p-value is greater than α. b-3. Interpret the results at α = 0.01. multiple choice 6 We conclude that the sample mean is greater than 73. We cannot conclude that the sample mean is greater than 73. We conclude that the population mean is greater than 73. We cannot conclude that the population mean is greater than 73.
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Consider the following hypotheses: H0: μ = 120 HA: μ ≠ 120 The population is normally distributed with a population standard deviation of 46. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic with x̄ = 132 and n = 50. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) a-2. What is the conclusion at the 5% significance level? multiple choice 1 Reject H0 since the p-value is less than the significance level. Reject H0 since the p-value is greater than the significance level. Do not reject H0 since the p-value is less than the significance level. Do not reject H0 since the p-value is greater than the significance level. a-3. Interpret the results at α = 0.05. multiple choice 2 We conclude that the population mean differs from 120. We cannot conclude that the population mean differs from 120. We conclude that the sample mean differs from 120. We cannot conclude that the sample mean differs from 120. b-1. Calculate the value of the test statistic with x̄ = 108 and n = 50. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) b-2. What is the conclusion at the 10% significance level? multiple choice 3 Reject H0 since the p-value is less than the significance level. Reject H0 since the p-value is greater than the significance level. Do not reject H0 since the p-value is less than the significance level. Do not reject H0 since the p-value is greater than the significance level. b-3. Interpret the results at α = 0.10. multiple choice 4 We conclude that the population mean differs from 120. We cannot conclude that the population mean differs from 120. We conclude that the sample mean differs from 120. We cannot conclude that the sample mean differs from 120.
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In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 4.8 and 0.8, respectively. (You may find it useful to reference the appropriate table: z-table or t-table) H0: μ ≤ 4.5 against HA: μ > 4.5 a-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) TEST STATISTIC = ___________? a-2. Find the p-value. multiple choice 1 p-value ≤ 0.01 0.01 < p-value ≤ 0.025 0.025 < p-value ≤ 0.05 0.05 < p-value ≤ 0.10 p-value > 0.10 a-3. At the 5% significance level, what is the conclusion? multiple choice 2 Reject H0 since the p-value is not greater than α. Reject H0 since the p-value is greater than α. Do not reject H0 since the p-value is not greater than α. Do not reject H0 since the p-value is greater than α. a-4. Interpret the results at α = 0.05. multiple choice 3 We conclude that the population mean is greater than 4.5. We cannot conclude that the population mean is greater than 4.5. We conclude that the population mean differs from 4.5. We cannot conclude that the population mean differs from 4.5. H0: μ = 4.5 against HA: μ ≠ 4.5 b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) TEST STATISTIC = ___________? b-2. Find the p-value. multiple choice 4 p-value ≤ 0.01 0.01 < p-value ≤ 0.025 0.025 < p-value ≤ 0.05 0.05 < p-value ≤ 0.10 p-value > 0.10 b-3. At the 5% significance level, what is the conclusion? multiple choice 5 Reject H0 since the p-value is not greater than α. Reject H0 since the p-value is greater than α. Do not reject H0 since the p-value is not greater than α. Do not reject H0 since the p-value is greater than α. b-4. Interpret the results at α = 0.05. multiple choice 6 We conclude that the population mean is greater than 4.5. We cannot conclude that the population mean is greater than 4.5. We conclude that the population mean differs from 4.5. We cannot conclude that the population mean differs from 4.5.
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