A sample of 50 chewable vitamin tablets have a sample mean of 230 milligrams of vitamin C. Nutritionists want to perform a hypothesis test to determine how strong the evidence is that the mean mass of vitamin C per tablet exceeds 225 milligrams. State the appropriate null and alternative hypotheses.
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- The population of healthy female adults, the mean red blood cell count (RBC) is 4.8 (millions of cells per cubic millimeter of whole blood). A researcher thinks the RBC is underestimated, so she conducts a test of significance using Null Hypothesis: µ ≤ 4.8 vs. Alternative Hypothesis: µ >4.8. If the true mean RBC is 4.75 and the null hypothesis is rejected, out of the four options below, what has occured? Type 1 Error, Type 2 Error, No error, OR can’t tell without knowing the degrees of freedom?A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.2 miles. Use a 0.05 significance level. Use the display to identify the null and alternative hypotheses, test statistic, and P-value. State the final conclusion that addresses the original claim. Hypothesis test results: p: Mean of variable Ho : µ = 2.2 HA: H> 2.2 Variable Sample Mean Length Std. Err. 2.38563 0.251663 499 0.737613 DF T-Stat P-value 0.2305is there evidence that the average infant mortality rate increases with teen birth rate? assume that the significance level is 0.05. i. state the null and alternative hypothesis. ii. should we reject or fail to reject the null? iii. justify using the rejection region
- Regulations from the Environmental Protection Agency say that soil used in play areas should not have lead levels that exceed a 400 parts per million (ppm). Before beginning construction at a new site, an agent will take a sample of soil and run a significance test on the mean lead level in the soil. If the mean lead level in the sample is significantly higher than 400 ppm, then the soil is deemed unsafe and construction cannot continue. Here are the hypotheses for this test: Ho : µ 400 ppm (soil is unsafe) (where u is the mean lead level in the soil at the new site). Which of the following would be a Type I error in this setting? Choose 1 answer: The soil is actually safe, and the sample result is below 400 ppm. so construction continues. The soil is actually safe, and the sample result is significantly higher than 400 ppm. so construction stops. The soil is actually unsafe, and the sample result is below 400 ppm, so construction continues. The soil is actually unsafe, and the sample…Big fish: A sample of 250 flounder of a certain species have sample mean weight 50.5 grams. Scientists want to perform a hypothesis test to determine how strong the evidence is that the mean weight is less than 49 grams. State the appropriate null and alternate hypotheses.A sample of 60 chewable vitamin tablets have a sample mean of 298 milligrams of vitamin C. Nutritionists want to perform a hypothesis test to determine how strong the evidence is that the mean mass of vitamin C per tablet differs from 299 milligrams. State the appropriate null and alternate hypotheses.
- A magazine reported that at the top 50 business schools in a region, students studied an average of 11.2 hours. Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the reported 11.2-hour benchmark. State the null and alternative hypotheses. Choose the correct answer below. A. H0: X=11.2 H1: X≠11.2 B. H0: μ=11.2 H1: μ≠11.2 C. H0: α≠11.2 H1: β=11.2 D. H0: α=11.2 H1: α≠11.2 E. H0: β≠11.2 H1: β=11.2 F. H0: β=11.2 H1: β≠11.2 G. H0:μ≠11.2 H1: μ=11.2 H. H0:μ≠11.2 H1: X=11.2 I. H0:μ=11.2 H1:X≠11.2 J. H0: X≠11.2 H1: X=11.2 K. H0:α≠11.2 H1: α=11.2 L. H0:α=11.2 H1:β≠11.2 What is a Type I error for your test? A. Concluding that the mean number of hours studied at your school is not different from the reported 11.2-hour benchmark when in fact it is not different B. Concluding that the…A data set includes data from 400 random tornadoes. The display from technology available below results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.3 miles. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. a. Identify the test statistic. (Round to two decimal places as needed.) b. Identify the P-value. (Round to three decimal places as needed.)A random sample of vehicle speeds were collected. Use the data to test the claim that the mean vehicle speed is more than 40 mph. Use a 0.05 level of significance. Sample data: x¯=42 mphs=7 mphn=34 Identify the tail of the test. Find the P-value Will the null hypothesis be rejected? Is the initial claim supported?
- In the past, the mean running time for a certain type of flashlight battery has been 9.6 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has decreased as a result. A hypothesis test is to be performed. Determine the null and alternative hypotheses. A. H0: µ ¥ 9.6 hours and H1: µ = 9.6 hours B. H0: µ = 9.6 hours and H1: µ ¥ 9.6 hours C. H0: µ = 9.6 hours and H1: µ > 9.6 hours D. H0: µ = 9.6 hours and H1: µ < 9.6 hoursThe dataset below that contains information on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions as well as cars with other transmissions. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average citymileage? 1. Set up the null and alternative hypotheses.2. Compute the test statistic.3. State the p-value for the test. State the decision and conclusion of the test in context. Feel free to use excel, Rstudio, or any other methods to answer the Question! Thanks Auto Manual 77 22 126 30 52 28 62 26 62 29 106 20 27 27 28 22 24 26 26 26 30 26 21 23 21 28 23 29 25 25 20 25 20 22 18 17 17 27 14 25 15 19 18 27 17 30 14 23 18 24 17 23 14 22 15 23 18 24 17 27 14 23 19 22 17 25 17 19 14 26 16 21 16 23 14 18 17 18 17 18 14 18 16 19 16 19 14 21 18 18…A data set includes data from 400 random tornadoes. The display from technology available below results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.6 miles. Use a 0.05 significance level. Use the display to identify the null and alternative hypotheses, test statistic, and P-value. State the final conclusion that addresses the original claim. Hypothesis test results: Mean of variable | Ho H=2.6 HAH>2.6 Variable Sample Mean Length 2.75311 Std. Err. DF 0.274284 399 T-Stat 0.558217 P-value 0.2885 OA. Fail to reject Ho. There is not sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles. OB. Reject Ho. There is not sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles. OC. Reject Ho. There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles OD. Fail to reject Ho. There is sufficient evidence to support…