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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Consider the following hypotheses: H0: μ = 410 HA: μ ≠ 410 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 = 421 and n = 85. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) a-2. What is the conclusion at the 10% significance level? Do not 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. Reject H0 since the p-value is greater than the significance level. Reject H0 since the p-value is less than the significance level. a-3. Interpret the results at α = 0.10. We cannot conclude that the population mean differs from 410. We conclude that the population mean differs from 410. We cannot conclude that the sample mean differs from 410. We conclude that the sample mean differs from 410. b-1. Calculate the value of the test statistic with x̄ = 397 and n = 85. (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 5% significance level? Reject H0 since the p-value is greater than the significance level. 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. Do not reject H0 since the p-value is less than the significance level. b-3. Interpret the results at α = 0.05. We conclude that the population mean differs from 410. We cannot conclude that the population mean differs from 410. We conclude that the sample mean differs from 410. We cannot conclude that the sample mean differs from 410.
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Consider the following hypotheses: H0: μ = 350 HA: μ ≠ 350 The population is normally distributed with a population standard deviation of 62. (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 = 367 and n = 40. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) a-2. What is the conclusion at the 1% significance level? Reject H0 since the p-value is less than the significance level. a-3. Interpret the results at α = 0.01. We conclude that the population mean differs from 350. b-1. Calculate the value of the test statistic with x̄ = 338 and n = 40. (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? Do not reject H0 since the p-value is greater than the significance level. b-3. Interpret the results at α = 0.10. We cannot conclude that the population mean differs from 350.
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Highway Accidents: Poisson Distribution A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Long-term history indicates that there has been an average of $1.72$ accidents per day on this section of the interstate. Let $r$ be a random variable that represents number of accidents per day. Let $O$ represent the number of observed accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information. (a) The civil engineer wants to use a Poisson distribution to represent the probability of $r$, the number of accidents per day. The Poisson distribution is $$ P(r)=\frac{e^{-\lambda} \lambda^{r}}{r !} $$ where $\lambda=1.72$ is the average number of accidents per day. Compute $P(r)$ for $r=0,1,2,3$, and 4 or more. (b) Compute the expected number of accidents $E=90 P(r)$ for $r=0,1,2,3$, and 4 or more. (c) Compute the sample statistic $\chi^{2}=\Sigma \frac{(O-E)^{2}}{E}$ and the degrees of freedom. (d) Test the statement that the Poisson distribution fits the sample data. Use a $1 \%$ level of significance.
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