A random sample of size n1=25, taken from a normal population with a standard deviation σ1=5, has a mean x̄1=80. A second random sample of size n2=36, taken from a different normal population with a standard deviation σ2=3, has a mean x̄2=75. Find a 99% confidence interval for μ1-μ2.
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A random sample of size n1=25, taken from a normal population with a standard deviation σ1=5, has a mean x̄1=80. A second random sample of size n2=36, taken from a different normal population with a standard deviation σ2=3, has a mean x̄2=75. Find a 99% confidence interval for μ1-μ2.
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- A random sample of 84 eighth grade students' scores on a national mathematics assessment test has a mean score of 290. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 285. Assume that the population standard deviation is 36. At α=0.07, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).Daily Driving The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 32 drivers over the age of 60 and finds that the mean number of miles driven is 22.9. The population standard deviation is 3.1 miles. At α=0.05, is there sufficient evidence that those drivers over 60 years old drive less than 24 miles per day on average? Assume that the variable is normally distributed. Use the P-value method with a graphing calculator. Find the P-value. Round it to four decimal places.In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?
- An electrical engineer wishes to compare the mean lifetimes of two types of transistors in an application involving high-temperature performance. A sample of 60 transistors of type A were tested and were found to have a mean lifetime of 1827 hours and a standard deviation of 174 hours. A sample of 180 transistors of type B were tested and were found to have a mean lifetime of 1658 hours and a standard deviation of 231 hours. Let ux represent the population mean for transistors of type A and µy represent the population mean for transistors of type B. Find a 95% confidence interval for the difference uy – µy . Round the answers to three decimal places. The 95% confidence interval isA researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVs equipped with tires made with compound 1 is 65 feet, with a population standard deviation of 13.6. The mean braking distance for SUVS equipped with tires made with compound 2 is 69 feet, with a population standard deviation of 8.5. Suppose that a sample of 55 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ₁ be the true mean braking distance corresponding to compound 1 and μ₂ be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance. Step 3 of 5 Find the p-value associated with the test statistic. Round your answer to four decimal places. Answer How to enter your answer (opens in…According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.34. Suppose a random sample of 109 traffic fatalities in a certain region results in 50 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the x = 0.01 level of significance? Because npo (1-Po) = 24.5 > 10, the sample size is (Round to one decimal place as needed.) What are the null and alternative hypotheses? p = 0.34 versus H₁: p > 0.34 Ho: p (Type integers or decimals. Do not round.) Find the test statistic, Zo. Zo = 2.62 (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) less than 5% of the population size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied.
- A certain IQ test is known to have a population mean of 100 and standard deviation of 15 in the general population. You want to test whether psychology majors have a different average IQ than the population as a whole. Assume the variance of IQ is the same for Psych majors as it is in the general population. Suppose that Psychology majors actually have an average IQ of 108. If you do a 2-tailed test at α= .05 with a sample of 56 Psychology majors, you will be able to reject the null hypothesis if the mean IQ of your sample is below [L] or above [H]. Find L and H values. Options listed below. [L] answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92. [H] Answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92.A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVs equipped with tires made with compound 1 is 65 feet, with a population standard deviation of 13.6. The mean braking distance for SUVs equipped with tires made with compound 2 is 69 feet, with a population standard deviation of 8.5. Suppose that a sample of 55 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ₁ be the true mean braking distance corresponding to compound 1 and μ₂ be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance. Step 5 of 5: State the conclusion of the hypothesis test. Answer Tables Keypad Keyboard Shortcuts Previous Step Answers There is sufficient evidence…
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