MATH 221 WEEK 6 QUIZ (100% CORRECT ANSWERS) | (GRADED A) Question and answer Solution | DeVry University.

(CO 5) A company claims that its heaters last more than 5 years. Write the null and alternative hypotheses and note which is the claim. Ho: μ = 5 (claim), Ha: μ ≥ 5 Ho: μ > 5 (claim), Ha: μ ≤ 5 Correct Answer Ho: μ ≤ 5, Ha: μ < 5 (claim) (CO 5) An executive claims that her employees spend no less than 2.5 hours each week in meetings. Write the null and alternative hypotheses and note which is the claim. Ho: μ ≤ 2.5 (claim), Ha: μ > 2.5 Correct Answer Ho: μ > 2.5, Ha: μ ≤ 2.5 (claim) Ho: μ = 2.5, Ha: μ ≥ 2.5 (claim) See text page 349 Question 3 0 / 2 pts (CO 5) In hypothesis testing, a key element in the structure of the hypotheses is that the alternative hypothesis has the . truth claim equality Correct Answer simple inequality (CO 5) A landscaping company claims that at most 90% of workers arrive on time. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? There is not sufficient evidence to support the claim that at least 90% of workers arrive on time There is not sufficient evidence to support the claim that at most 90% of workers arrive on time There is sufficient evidence to support the claim that a least 90% of workers arrive on time Correct! There is sufficient evidence to support the claim that at most 90% of workers arrive on time (CO 5) A textbook company claims that their book is so engaging that less than 55% of students read it. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? There is not sufficient evidence to support the claim that no more than 55% of students read this text There is sufficient evidence to support the claim that no more than 55% of students read this text There is sufficient evidence to support the claim that less than 55% of students read this text Correct Answer There is not sufficient evidence to support the claim that less than 55% of students read this text (CO 5) An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 miles per hour. In a test of 45 of these tires, the braking distance has a mean of 77 and a standard deviation of 5.9 feet. Find the standardized test statistic and the corresponding p-value. Correct! z-test statistic = 2.27, p-value = 0.0230 z-test statistic = -2.27, p-value = 0.0230 z-test statistic = -2.27, p-value = 0.0115 z-test statistic = 2.27, p-value = 0.0115 See text page 365 (CO 5) The heights of 82 roller coasters have a mean of 281.4 feet and a standard deviation of 59.3 feet. Find the standardized tests statistics and the corresponding p-value when the claim is that roller coasters are less than 290 feet tall. z-test statistic = 1.31, p-value = 0.0964 z-test statistic = -1.31, p-value = 0.1891 z-test statistic = 1.31, p-value = 0.1891 Correct! z-test statistic = -1.31, p-value = 0.0964 See text page 365 (CO 5) A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A random sample of 51 light bulbs as a mean of 712.8 hours with a population standard deviation of 62 hours. At an α=0.05, can you support the company’s claim using the test statistic? Claim is the null, reject the null and cannot support claim as test statistic (-0.83) is in the rejection region defined by the critical value (-1.645) Claim is the alternative, reject the null and support claim as test statistic (-0.83) is not in the rejection region defined by the critical value (-1.96) Claim is the alternative, fail to reject the null and cannot support claim as the test statistic (-0.83) is in the rejection region defined by the critical value (-1.96) Correct! Claim is the null, fail to reject the null and support claim as test statistic (-0.83) is not in the rejection region defined by the critical value (-1.645) (CO 5) A restaurant claims the customers receive their food in less than 16 minutes. A random sample of 39 customers finds a mean wait time for food to be 15.8 minutes with a population standard deviation of 4.9 minutes. At α = 0.04, what type of test is this and can you support the organizations’ claim using the test statistic? Claim is the null, reject the null so cannot support the claim as test statistic (-0.25) is in the rejection region defined by the critical value (-2.05) Correct! Claim is the alternative, fail to reject the null so cannot support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75) Claim is the alternative, reject the null so support the claim as test statistic (-0.25) is in the rejection region defined by the critical value (-2.05) Claim is the null, fail to reject the null so support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75) (CO 5) A manufacturer claims that their calculators are 6.800 inches long. A random sample of 39 of their calculators finds they have a mean of 6.812 inches with a standard deviation of 0.05 inches. At α=0.08, can you support the manufacturer’s claim using the p value? Claim is the alternative, fail to reject the null and support claim as p-value (0.067) is less than alpha (0.08) Claim is the null, reject the null and cannot support claim as p-value (0.067) is less than alpha (0.08) Correct! Claim is the null, fail to reject the null and support claim as p-value (0.134) is greater than alpha (0.08) Claim is the alternative, reject the null and cannot support claim as p-value (0.134) is greater than alpha (0.08) (CO 5) A travel analyst claims that the mean room rates at a three-star hotel in Chicago is greater than $152. In a random sample of 36 three-star hotel rooms in Chicago, the mean room rate is $165 with a population standard deviation of $41. At α=0.10, can you support the analyst’s claim using the p-value? Claim is the null, reject the null as p-value (0.029) is less than alpha (0.10), and cannot support the claim Claim is the null, fail to reject the null as p-value (0.029) is less than alpha (0.10), and cannot support the claim Claim is the alternative, fail to reject the null as p-value (0.029) is less than alpha (0.10), and can support the claim Correct! Claim is the alternative, reject the null as p-value (0.029) is less than alpha (0.10), and can support the claim (CO 5) A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 3.5 miles per gallon. At α=0.05, can you support the company’s claim assuming the population is normally distributed? Correct! Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported Yes, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported No, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported (CO 5) A state Department of Transportation claims that the mean wait time for various services at its different location is more than 6 minutes. A random sample of 16 services at different locations has a mean wait time of 9.5 minutes and a standard deviation of 7.6 minutes. At α=0.01, can the department’s claim be supported assuming the population is normally distributed? Yes, since p of 0.043 is less than 0.09, reject the null. Claim is alternative, so is supported Correct! No, since p of 0.043 is greater than 0.01, fail to reject the null. Claim is alternative, so is not supported Yes, since p of 0.043 is greater than 0.01, fail to reject the null. Claim is null, so is supported No, since p of 0.043 is greater than 0.01, reject the null. Claim is null, so is not supported (CO 5) A used car dealer says that the mean price of a three-year-old sport utility vehicle in good condition is $18,000. A random sample of 20 such vehicles has a mean price of $18,450 and a standard deviation of $1860. At α=0.08, can the dealer’s claim be supported assuming the population is normally distributed? Correct! Yes, since the test statistic of 1.08 is not in the rejection region defined by the critical value of 1.85, the null is not rejected. The claim is the null, so is supported No, since the test statistic of 1.08 is close to the critical value of 1.24, the null is not rejected. The claim is the null, so is supported Yes, since the test statistic of 1.08 is in the rejection region defined by the critical value of 1.46, the null is rejected. The claim is the null, so is supported No, since the test statistic of 1.08 is in the rejection region defined by the critical value of 1.85, the null is rejected. The claim is the null, so is not supported See text pages 379-380 (CO 5) A researcher wants to determine if eating more vegetables helps high school juniors learn algebra. One junior class has extra vegetables and another junior class does not. After 2 weeks, the entire both classes take an algebra test and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups? That the group without extra vegetables receives different instruction Correct! That each pair of students has similar IQs or abilities in mathematics That each class of students has similar ages at the time of the testing That each class has similar average IQs or abilities in mathematics (CO 5) Assuming the population is normally distributed, test the claim that the mean is more than 23 using an α of 0.05. The sample statistics are a mean of 24.9, standard deviation of 2.11, and an n of 9. The data support the claim, as the null was not rejected and the claim is the null. The data do not support the claim, as the null was rejected and the claim is the alternative. The data do not support the claim, as the null was not rejected and the claim is the null. Correct! The data support the claim, as the null was rejected and the claim is the alternative. (CO 5) A company claims that the hold times for customer service averages at most 10 minutes. A random sample of 24 hold times has a mean of 11.2 minutes with a standard deviation of 3.4 minutes. Is there enough evidence to support the claim at α = 0.05? Assume the population is normally distributed. Correct Answer No, since p of 0.049 is less than 0.05, reject the null. Claim is null, so is not supported Yes, since p of 0.049 is greater than 0.05, fail to reject the null. Claim is null, so is supported No, since p of 0.049 is greater than 0.05, fail to reject the null. Claim is alternative, so is not supported Yes, since p of 0.049 is less than 0.05, reject the null. Claim is null, so is supported (CO 5) A coach claims that all players can run more than 1.5 miles. A random sample of 17 players finds that they can run an average of 1.7 miles with a standard deviation of 0.4 miles. Is there enough evidence to support the claim at α of 0.01? Assume the population is normally distributed. Yes, since p of 0.028 is less than 0.01, reject the null. Claim is null, so is supported Correct Answer No, since p of 0.028 is greater than 0.01, fail to reject the null. Claim is alternative, so is not supported Yes, since p of 0.028 is greater than 0.01, reject the null. Claim is alternative, so is supported No, since p of 0.028 is less than 0.01, reject the null. Claim is alternative, so is not supported