Find the P-value for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject H0 for the given level of significance α. Two-tailed test with test statistic z=−1.86 and α=
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- Do campers with trailers really get better mileage per gallon on the highway? The table shows results from a study of the MPG (miles per gallon) of campers with trailers both in the mountains and on desert roads. Assume that the two samples are randomly selected, independent, the population standard deviations are not know and not considered equal. At the 0.05 significance level, test the claim that the mpg on desert roads is better than in the mountains. MPG on Desert Roads 30.9 32.6 28.4 25.4 35.1 32.4 31.1 30.9 34.1 35.5 MPG in the Mountains 24 21.2 22.3 24.9 23.2 24.2 25.1 25.8 23.1 28.1 What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) Hg: Select an answer v Select an answer H: Select an answer ? v Select an answer v Original Claim = Select an answer v df =An alternative proof of Theorem 2 may be based on the fact that if X1, X2, ..., and Xn are independent ran-dom variables having the same Bernoulli distribution with the parameter θ, then Y = X1 + X2 +···+ Xn isa random variable having the binomial distribution withthe parameters n and θ.Verify directly (that is, without making use of the factthat the Bernoulli distribution is a special case of thebinomial distribution) that the mean and the variance ofthe Bernoulli distribution are μ = θ and σ2 = θ (1 − θThe mean number of eggs per person eaten in the United States is 244. Do college students eat a different number of eggs than the average American? The 60 college students surveyed averaged 255 eggs per person and their standard deviation was 64.4. What can be concluded at the a = 0.10 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Но: 244 H1: PV A 244 c. The test statistic 1.323 (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 ? Va f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest that the populaton mean is significantly different from 244 at a = 0.10, so there is statistically significant evidence to conclude that the population mean number of eggs consumed by college students per year is different from 244. O The data suggest that the…
- Two treatments for a new infectious disease have been developed to reduce hospitalizations. Each treatment was given to different groups of patients. Treatment 1 was given to 65 people. Subjects of treatment 1 had a mean hospital stay of 5.6 days with a standard deviation of 2.6 days. Treatment 2 was given to 54 people. Subjects of treatment 2 had a mean hospital stay of 8.4 days with a standard deviation of 3.0 days. Use the method of hypothesis testing to test the claim that the mean time in the hospital for treatment 1 is shorter than the mean time in the hospital for treatment 2 assuming a 0.05 significance level. (a) List the null and alternative hypotheses for this test. (b) Compute the value of the test statistic (c) Determine the rejection region.(d) Determine whether or not we can reject the null hypothesis.Q5. With 0.05 significance level, H1: p > 0.5, and the value of test statistic is z = 1.93. Then theP-value is equal to 0.9732.a. Trueb. FalseA random sample of 818 births included 435 boys. Use a 0.05 significance level to test the claim that 50.6% of newborn babies are boys. Do the results support the belief that 50.6% of newborn babies are boys? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. H0: p=0.506 H1: p>0.506 B. H0: p≠0.506 H1: p=0.506 C. H0: p=0.506 H1: p≠0.506 D. H0: p=0.506 H1: p<0.506 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is: (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is : (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. A. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that 50.6% of newborn babies are boys. B.Fail to reject H0. There is sufficient evidence to…
- Starting Salaries. Starting annual salaries for business school graduates majoring in finance and management information systems (MIS) were collected in two independent random samples summarized below. Based on previous studies, the population standard deviations for finance and MIS salaries are estimated to be $2,100 and $2,600, respectively. Use both the critical value and p-value approaches to conduct the hypothesis test. At a .05 level of significance, what is your conclusion?The mean number of eggs per person eaten in the United States is 266. Do college students eat a different number of eggs than the average American? The 61 college students surveyed averaged 285 eggs per person and their standard deviation was 72.6. What can be concluded at the a= 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Но: v Select an answer H.: vSelect an answer c. The test statistic ? (please show your answer to 3 decimal places.) d. The p-value = e. The p-value is ? f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... (Please show your answer to 4 decimal places.) a O The data suggest that the sample mean is not significantly different from 266 at a = 0.10, so there is statistically insignificant evidence to conclude that the sample mean number of eggs consumed by college students per year is different from 285. O The data suggest that the…A custodian wishes to compare two competing floor waxes to decide which one is best. He believes that the mean of WaxWin is less than the mean of WaxCo. In a random sample of 20 floors of WaxWin and 17 of WaxCo. WaxWin had a mean lifetime of 26.4 with a standard deviation of 8.6 and WaxCo had a mean lifetime of 27.2 with a standard deviation of 6.6. Perform a hypothesis test using a significance level of 0.05 to help him decide. Let WaxWin be sample 1 and WaxCo be sample 2 The correct hypotheses are: Ο Ηο: μι < με HA₁₂(claim) Ο Ηρ: με 2 με HA: 1₂(claim) O Ho: ₁ = ₂ HAM12(claim) Since the level of significance is 0.05 the critical value is -1.69 (round to 3 places) The test statistic is: The p-value is: (round to 3 places)
- In the past, the time for Jeff's journey to work had mean 45.7 minutes and standard deviation 5.6 minutes. This year he is trying a new route. In order to test whether the new route has reduced his journey time, Jeff finds the mean time for a random sample of 30 journeys using the new route. He camies out a hypothesis test at the 2.5% significance level. Jeff assumes that, for the new route, the joumey time has a nomal distribution with standard deviation 5.6 minutes. (a) State appropriate null and alternative hypotheses for the test. (b) Determine the rejection region for the test.The Woodcock-Johnson Cognitive Ability (WJCA) test indicates that the average score is 95. The same group of 12th grade students (n = 72) in Columbus are tested and the sample mean is 110.1 and the sample standard deviation is 15.2. Do the scores provide good evidence that the mean WJCA score of this population is greater than 95? State the null (H0) and alternative (Ha) hypotheses. 2. What are the confidence intervals for this data? 3. What is the value of the test statistic? 4. What is the p-value for this data? 5. What is your decision about the null hypothesis?: Reject Fail to Reject 6. Summarize the conclusion in the context of the problem.Suppose a recent study of Trucks and SUVs gave an average fuel efficiency of 19.2 mpg for Trucks and 21.4 mpg for SUVs. The sample standard deviation for Trucks was 3.2 mpg and 2.8 mpg for SUVs. These results were based on samples of 35 Trucks and 39 SUVs. At the 1% significance level, can we conclude that, on average, SUVs have better fuel efficiency than Trucks? Clearly state the null and alternative hypotheses, use the critical value approach (draw a detailed picture), and write out a detailed conclusion. Organize: Hypotheses: Detailed picture: Detailed conclusion: