The hypothesis test H0:μ1−μ2=2.6 H1:μ1−μ2≠2.6 is to be carried out for population 1 and 2 where σ1 and σ2 are not known. A random sample of 44 from population 1 has a mean of 89.2 and a standard deviation of 9.9. A random sample of 29 from population 2 has a standard deviation of 7.2. The test statistic was found to be tc=0.94821. What was the mean of the sample from population 2? x¯2 =
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The hypothesis test
H0:μ1−μ2=2.6
H1:μ1−μ2≠2.6
is to be carried out for population 1 and 2 where σ1 and σ2 are not known. A random sample of 44 from population 1 has a
x¯2 =
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- Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of μ=8 parts per billion (ppb) is considered safe for agricultural use. A well in Los Banos is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of x=7.3 ppb arsenic. It is known that σ=1.9 ppb for this type of data. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use the classical approach. Use α=0.01 What is the hypotheses for this problem? A: Ho μ =7.3ppb vs HA μ < 7.3ppb B: Ho μ <7.3ppb vs HA μ ≥ 7.3ppb C: Ho μ =8.0ppb vs HA μ < 8.0ppb D: Ho μ <8.0ppb vs HA μ ≥ 8.0ppbThe braking ability was compared for two car models. Random samples of two cars were selected. The first random sample of size 64 cars yield a mean of 36 and a standard deviation of 8. The second sample of size 64 yield a sample mean of 33 and a standard deviation of 8. Do the data provide sufficient evidence to indicate a difference between the mean stopping distances for the two models? Use Alpha= 0.01. Ho: µ1 – µ2 = 0 vs. Ha: µ1 – µ2 + 0 .p-value = 0.0017. Reject Ho Но: Д, — м2 — 0 vs. Ha:M1 — M2 + 0. p-value — 0.034. Ассеpt Ho O Ho:µ1 – Hz Но: И — 2 — 0 vs. Ha:M, — нz + 0. p-value —D 0.0017. Ассept Ho Ho: H1 – U2 = 0 vs. Ha: µ1 – µ2 + 0. p-value = 0.034. Reject HoA random sample of 81 tourists in Chattanooga showed that they spent an average of $2000(in a week) with a standard deviation of $100 and a sample of 64 tourists in Ontario showed that they spent an average of $2500(in a week) with a standard deviation of $144. We are interested in determining if there is any significant difference between the average expenditures of those who visited the two cities? Test the hypothesis at alpha=0.05 and write all the steps.
- A researcher wishes to see if there is a difference in the cholesterol levels of two groups of men. A random sample of 30 men between the ages of 25 and 40 is selected and tested. The average level is 223. A second random sample of 25 men between the ages of 41 and 56 is selected and tested. The average of this group is 229. The population standard deviation for both groups is 6. At α = 0.01, is there a difference in the cholesterol levels between the two groups? Assume that the population is normally distributed. Required Steps: Step 1: Label all given information. Step 2:State the null and alternative hypothesis and identify the claim. Step 3:Verify that the conditions are met to perform the test. Step 4:Sketch the normal distribution and find the critical regions. Step 5:Compute the test statistic. Step 6:Make a decision Step 7:Summarize the results.The personality trait of "Conscientiousness" (someone who is organized, responsible, and can control their impulses) has μ = 120 and σ =9. Test whether ARC students (n = 9, M = 126) differ on Conscientiousness. α = .05. zM (z score for the sample mean) =A random sample is selected from a normal population with a mean of μ = 30 and a standard deviation of σ = 8. After treatment is administered to the individuals in the sample, the sample mean is found to be M = 33. If the sample consists of n = 16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. If the sample consists of n = 64 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. Comparing your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.
- To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.7 feet. The mean braking distance for Make B is 44feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e). a) identify the claim and state Ho and Ha b) find the critical values and identify the rejection regions c) Find the standardized test statistic z d) Decide whether to reject or fail to reject the null hypothesis. e) Interpret the decision in the context of the original claim.A researcher was doing a study for a new Coronavirus Drug and conducted a hypothesis test like this one: H0: μμ = 15 Ha: μμ ≠≠ 15 a. What type of test is this? two-tailed left-tailed right-tailed b. She obtained a test statistic of -1.21, with a p-value of 0.245. So she concluded that her true mean must be equal to 15. Is this interpretation correct? Yes No Why or why not? (Will be graded manually!)vA random sample of 76 eighth grade students' scores on a national mathematics assessment test has a mean score of 283. 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 280. Assume that the population standard deviation is 31. At α=0.04, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).