A random sample of size n₁ = 23, taken from a normal population with a standard deviation 01 = 6, has a mean x₁ = 89. A second random sample of size n₂ = 39, taken from a different normal population with a standard deviation 6₂ = 4, has a mean x₂ = Find a 96% confidence interval for μ₁-₂. = 31. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The confidence interval is
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- Ann thinks that there is a difference in quality of life between rural and urban living. She collects information from obituaries in newspapers from urban and rural towns in Idaho to see if there is a difference in life expectancy. A sample of 3 people from rural towns give a life expectancy of xr¯=79��¯=79 years with a standard deviation of sr=7.57��=7.57 years. A sample of 14 people from larger towns give xu¯=82��¯=82 years and su=5.48��=5.48 years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 5% level of significance. (a) State the null and alternative hypotheses: (Type ‘‘mu_r′′‘‘��_�″ for the symbol μr�� , e.g. mu_rnot=mu_u��_����=��_� for the means are not equal, mu_r>mu_u��_�>��_� for the rural mean is larger, mu_r<mu_u��_�<��_� , for the rural mean is smaller. )H0�0 = equation editor Equation Editor Ha�� = equation editor Equation Editor (b) The degree of…Unfortunately, arsenic occurs naturally in some ground water.† A mean arsenic level of μ = 8.3 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 41 tests gave a sample mean of x = 7.3 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8.3 ppb? Use ? = 0.01. (a) What is the level of significance? State the null hypotheses H0 and the alternate hypothesis H1 . H0 : μ ---Select--- < ≥ ≤ = > ≠ H1 : μ ---Select--- < > ≤ ≥ = ≠ (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown. The Student's t, since the…According to the historical data, the life expectancy in Belgium is less than the life expectancy in the United States. A new study has been made to see whether this has changed. Records of 260 individuals from Belgium who died recently are selected at random. The 260 individuals lived a mean of 78.4 years with a standard deviation of 8.8 years. Records of 285 individuals from the United States who died recently are selected at random and independently. The 285 Individuals lived a mean of 76.5 years with a standard deviation of 7.4 years. Assume that the population standard deviations of lifetimes in these two countries can be estimated by the sample standard deviations, as the samples used were quite large. Construct a 95% confidence interval for ₁-₂, the difference between the life expectancy μ₁ in Belgium and the life expectancy μ₂ in the United States. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three…
- The null hypothesis: H, :0 The alternative hypothesis: H :0 The type of test statistic: (Choose one) v The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.05 level of significance: (Round to at least three decimal places.) Can we support the claim that the life expectancy in the United States is greater than the life expectancy in Ireland? O Yes NoAccording to the historical data, the life expectancy in the United States is less than or equal to the life expectancy in Ireland. A new study has been made to see whether this has changed. Records of 235 individuals from the United States who died recently are selected at random. The 235 individuals lived an average of 77.6 years with a standard deviation of 6.7 years. Records of 220 individuals from Ireland who died recently are selected at random and independently. The 220 individuals lived an average of 76.3 years with a standard deviation of 5.5 years. Assume that the population standard deviations of the life expectancies can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.1 level of significance, is there enough evidence to support the claim that the life expectancy, u,, in the United States is greater than the life expectancy, µ, in Ireland? Perform a one-tailed test. Then fill in the table below. Carry…A manufacturer of bolts has a quality control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality control engineer knows that the bolts coming off the assembly line have a mean length of 8cm with a standard deviation of 0.05 cm. For what length will a bolt be destroyed?
- Suppose that heights of 10-year-old boys in the US vary according to a normal distribution with mean of 138 cm and standard deviation of 7. Compute the Z-score for a boy with height of 150 cm and find the correct interpretations. a. Boy's height is 0.71 standard deviation lower the national average b. Boy's height is 1.71 standard deviation above the national average c. Boy's height is 1.71 standard deviation lower than the national average d. Boy's height is 2.71 standard deviation above the national averageA random sample of 100 automobile owners in a region shows that an automobile is driven on average 25,500 kilometers per year with a standard deviation of 3500 kilometers. Assume the distribution of measurements to be approximately normal. Construct a 90% prediction interval for the kilometers traveled annually by an automobile owner in the region. Click here to view page 1 of the standard normal distribution table. of the standard normal distribution table. Click here to view page 2 Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. The prediction interval is < X < (Round to the nearest integer as needed.) -CIt takes an average of 14.5 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will increase if the patient is immediately told the truth about the injury. The EMT randomly selected 70 injured patients to immediately tell the truth about the injury and noticed that they averaged 16.3 minutes for their blood to begin clotting after their injury. Their standard deviation was 4.75 minutes. What can be concluded at the the α = 0.10 level of significance? a. For this study, we should use [Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer H₁: ? Select an answer ✓ c. The test statistic ? = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? ✓ a f. Based on this, we should [Select an answer the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the populaton mean is significantly greater than 14.5 at a = 0.10, so…
- It takes an average of 14 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will change if the patient is immediately told the truth about the injury. The EMT randomly selected 43 injured patients to immediately tell the truth about the injury and noticed that they averaged 12.5 minutes for their blood to begin clotting after their injury. Their standard deviation was 3.1 minutes. What can be concluded at the the αα = 0.01 level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly different from 14 at αα = 0.01, so there is statistically significant…A car company says that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 8 cars has a mean gas mileage of 21 mpg and a standard deviation of 4 mpg. At a= 0.025, test the company's claim. Assume the population is normally distributed. Click here to view the t-distribution table. Click here to view page 1 of the normal table. Click here to view page 2 of the normal table. %3D State the appropriate hypotheses to test. ΟΑ. Η μ5 23 H p> 23 YB. H, p2 23 H. p<23 OC. Ho =23 H u#23 OD. H, p 23 H, p=23 What is the value of the standardized test statistic? The standardized test statistic is (Round to two decimal places as needed.)A random sample of 12 graduates of a certain secretarial school typed an average of 82.6 words per minute with a standard deviation of 8.1 words per minute. Assuming a normal distribution for the number of words typed per minute, find a 95% confidence interval for the average number of words typed by all graduates of this school. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. The confidence interval is <μ< (Round to two decimal places as needed.)