Question;1. (6 points) Recent talks amongst lawmakers suggested giving tax breaks to automakers whose cars haveaverage gas mileages exceeding 31mpg. A random sample of 35 vehicles produced by a major automaker wastaken, and the average gas mileage for these vehicles was 31.65 mpg, with a standard deviation of 0.81 mpg.Using the.05 level of significance, is there evidence to suggest that this company would get the tax break if thelaw passed?State Hypotheses:Test Statistic Value:P-value:Decision:Using plain language, interpret your statistical decision.1b. In words, what does the represent in the hypothesis above?a. The proportion of the population of this companys cars that would qualify for a tax breakb. The average gas mileage of the 35 vehiclesc. The average gas mileage of all vehicles on the roadd. The average gas mileage of all vehicles produced by this particular companye. The average gas mileage of all vehicles sampled2. (6 points) A company specializes in preparing students for a particular exam by offering a one-day trainingcourse. The company claims that 80% of students who take their course will pass the exam. 41 out of 62students who recently took the course ended up passing the exam. Using the.05 level of significance, does thisprovide significant evidence to suggest the percentage who pass the exam is actually lower than the companyclaims?State Hypotheses:Test Statistic Value:P-value:Decision:Using plain language, interpret your statistical decision.2b. What type of error may have been committedType I or Type II?3. Suppose you are interested in estimating the percentage of Americans who feel that the common cold viruscan be avoided by wearing warm clothing outside when temperatures are low. You would like to estimate thispercentage with 90% confidence and a margin of error of only 3%. Determine how many Americans youshould randomly sample.4. A random sample of students is to be taken to try and estimate the average amount of money spent ontextbooks in a semester. The publisher that is financing the study would like to estimate the average with 95%confidence and a margin of error of $10. It is estimated that the standard deviation of amounts spent ontextbooks is $50. Use this information to determine how many students should be randomly selected for thisstudy.5. (6 points) Your company purchases rubber washers. It is extremely important that the diameter of the holein the middle of the washer be no different than 0.5 inch. If it is different, the shipment must be returned to themanufacturer. You have just received a shipment of 10,000 washers. Theres no way to measure the entirepopulation, so you take a random sample of 35 of them. The sample mean diameter is 0.45 inches, and thestandard deviation is calculated to be 0.12 inch. Given this information, is there evidence to suggest that themean diameter of the entire shipment is something other than what it should be? Use the.05 level ofsignificance to make your decision.State hypotheses:Test Statistic Value:P-valueDecision:Decision Time: Interpret your statistical decision by stating whether or not the shipment should be returned tothe sender.6. A hypothesis test was conducted. The shaded portion in the picture below represents what?a. The Z value for the test of the hypothesis Ha:b. The T value for the test of the hypothesis Ha:c. The P-value for the test of the hypothesis Ha: pd. The P-value for the test of the hypothesis Ha:e. The P-value for the test of the hypothesis Ha: p7. A study was conducted to see if people could successfully remove warts using duct tape instead of theconventional method used by doctors where the warts are frozen off using liquid nitrogen. Patients at MadiganArmy Medical Center were randomly assigned to one of the treatment methodsduct tape or liquid nitrogen.Of the 104 in the duct tape group, 88 had their wart successfully removed. Of the 100 in the liquid Nitrogengroup, 60 of them had their wart successfully removed. Create a 95% confidence interval estimating thedifference in percentage of successful outcomes for the two groups, p1 p 2. Please write your final answer inpercentage form rather than as proportions.(,)7b. Which of the following can you conclude:a. There appears to be a significant difference between the population percentages.b. There does not appear to be a significant difference between the population percentages.c. If a hypothesis test would have been carried out, the null would have been rejected at the.05 level of significanced. choices a and c are both truee. choices b and c are both true8. A real estate agent wanted to carry out a formal test to see if the average selling price differed for homeswith garages and those without garages.Which of the following best identifies the impact of a Type II error for this test?a. The real estate agent concludes that no significant difference exists, but in actuality, there is adifference in the average selling prices.b. The real estate agent concludes that a significant difference exists, but in actuality, there is nodifference in the average selling prices.c. The real estate agent concluded that a significant difference exists, and in actuality, there isa significant difference in the average selling prices.d. The real estate agent concluded that no significant difference exists, and in actuality, there isnot a significant difference in the average selling prices.9. A test is carried out to see if the mean diameter of circular crawlspaces in a building is less than 18 inches.The P-value for the test turned out to be 0.4390, which was based on a sample mean of 17.91 inches. Based onthis, which of the following can you conclude?a.b.c.d.The mean diameter of all of the crawlspaces is not 18 inchesThere is evidence to suggest that the mean diameter is something other than 18 inches.All we can say is that the mean diameter of all of the crawlspaces is less than 18 inches.There is no evidence to suggest the mean diameter of all of the crawlspaces less than 18 inches.10. An auto manufacturer needs to test to see if the percentage of its airbags that are defective is greater than2%. If it is found to be higher than 2%, production must be halted until the problem is corrected. Which typeof error would be more detrimental for the consumers of this company's automobiles (in terms of safety)?a. Type Ib. Type IIc. Neither, as long as they do all of their calculations correctly, there should be no error.d. Neither would be bad for the consumer, but both would be bad for the manufacturer.11. In the book Business Research Methods, the authors discuss a manager who compares the effectiveness oftwo types of training of salespeople by conducting a completely randomized comparative experiment. Twentyone people got randomly assigned to receive training method A, and thirty-four people got assigned to trainingmethod B. After the training, all people are assigned to their respective stores, and work for the next year. Atyears end, the average weekly sales for the salespeople are compared, based on the type of training theyreceived (method A or B). The weekly sales averages and standard deviations are given below. Use theinformation to test whether a significant difference exists between the average sales for the two trainingmethods.s A: 225x A: 1590.00n A: 21s B: 251x B: 1372.00n B: 34State Hypotheses:Test Statistic Value:P-value:Using plain language, state how much evidence, if any, exists to suggest a significant difference in averages.12. Which of the following is the correct result for the hypothesesH 0: 2.20and the confidence intervalHa: 2.20(1.973, 2.318)? Assume that the alpha level for the test is.01 and the confidence level was 99%.a.b.c.d.The null hypothesis should be rejected, and therefore, a Type II error may be committed.The null hypothesis should be rejected, and therefore, a Type I error may be committed.The null hypothesis should not be rejected, and therefore, a Type I error may be committedThe null hypothesis should not be rejected, and therefore, a Type II error may be committed12B. The confidence interval above is to be used to decide if the average value for a shipment of coffeedispensers weights differs from 2.20 pounds. If you have evidence to suggest that it does differ from 2.20pounds, the shipment cannot be sent using standard procedures. Decision Time: Will you be sending theshipment using standard procedures?
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