St. Petersburg College | STA 2023 – ELEMENTARY STATISTICS | Module 5 Answered Test |

n 1 1 Select the most appropriate response. It is claimed that the mean age of bus drivers in Chicago is 50.2 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? Question options: There is not sufficient evidence to support the claim μ = 50.2. There is not sufficient evidence to reject the claim μ = 50.2. There is sufficient evidence to support the claim μ = 50.2. There is sufficient evidence to reject the claim μ = 50.2. on Select the most appropriate response. It is claimed that the mean age of bus drivers in Chicago is 59.3 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? Question options: There is not sufficient evidence to reject the claim μ = 59.3. There is sufficient evidence to reject the claim μ = 59.3. There is not sufficient evidence to support the claim μ = 59.3. There is sufficient evidence to support the claim μ = 59.3. on Select the most appropriate response. In hypothesis testing, what is the function of a critical value that is obtained from the tables? Question options: It is equal to the calculated statistic from the observed data. St. Petersburg College | STA 2023 – ELEMENTARY STATISTICS | Module 5 Test | It is the point on the number line where the decision changes from reject to fail to reject. It is the center of the distribution of X's. It is the point that is 1 standard deviation away from the mean. on Determine the critical value. Using the z-tables (or t-tables), determine the critical value for the left-tailed z-test with α=0.01. Question options: -2.326 2.326 2.576 -2.576 on Select the most appropriate response. Which type of alternative hypothesis would have the critical region shown in the figure below? Question options: H1:μ≠k H1:μ<k H1:μ>k H1:μ=k onTrue or False. If the p-value is less than alpha, the null hypothesis should be rejected. Question options: True False on Select the most appropriate response. What type of error is made if you reject the null hypothesis when the null hypothesis is actually true? Question options: Type I error Type II error significant error critical error on Select the most appropriate response. What type of error is made if you fail to reject the null hypothesis when the null hypothesis is actually false? Question options: Type I error Type II error significant error critical error onIdentify the correct null and alternative hypotheses. A hypnosis program designed to help individuals quit smoking claims a 57% success rate. A consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. What are the appropriate null and alternative hypotheses? Question options: H0: p = 0.57 vs. Ha: p < 0.57 H0: p = 0.57 vs. Ha: p > 0.57 H0: p = 0.57 vs. Ha: p ≠ 0.57 H0: p < 0.57 vs. Ha: p > 0.57 on Calculate the test statistic. A research company claims that no more than 55% of Americans regularly watch FOX News. You decide to test this claim and ask a random sample of 425 Americans if they watch this network regularly. Of the 425 sampled, 255 respond yes. Calculate the test statistic for the hypothesis test. Question options: -2.07 1.645 -1.96 2.07 None of the above. on Calculate the p-value. An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Determine the p-value for a test of the airline's claim. Question options:0.1499 0.0746 0.1230 0.0600 0.3508 on Select the most appropriate response. Five years ago, a survey found that the proportion of city employees who commute to work by car is 8%. A local city commissioner claims that the percentage is higher than it was five years ago. Data on employee commuting by car was collected on a random sample of 1000 employees and found 12% of employees commute by car. Test an appropriate hypothesis and state your conclusion at the 10% level of significance. State the alternative hypothesis, the test statistic, your decision and your findings. Note: The p-value is 0.. Question options: HA: p = 0.08; z = 4.66; Do not reject the null hypothesis. This data does not show a proportion in car commuting greater than 8%. HA: p > 0.08; z = 4.66; Reject the null hypothesis. This data shows a proportion in car commuting greater than 8%. HA: p < 0.08; z = -4.66; Reject the null hypothesis. This data does not show a proportion in car commuting greater than 8%. HA: p > 0.08; z = -4.66; Do not reject the null hypothesis. This data shows a proportion in car commuting greate than 8%. HA: p < 0.08; z = 4.66; Reject the null hypothesis. This data does not show a proportion in car commuting greater than 8%. on State your conclusion to the hypothesis test. The mayor of a certain city is tasked with cutting over 5 million dollars out of next year’s budget and is considering cuts to spending on public transportation. Themayor decides to conduct a hypothesis test and will only cut spending on public transportation if fewer than 15% of residents use the service. In a random sample of 300 residents, 36 reported that they did use public transportation. Perform the appropriate hypothesis test at a 1% significance level. Question options: Reject the null hypothesis. There is sufficient evidence to conclude that fewer than 15% of residents use public transportation. Reject the null hypothesis. There is sufficient evidence to conclude that more than 15% of residents use public transportation. Do not reject the null hypothesis. There is insufficient evidence to conclude that more than 15% of residents us public transportation. Do not reject the null hypothesis. There is insufficient evidence to conclude that fewer than 15% of residents use public transportation. on Identify the correct alternative hypothesis. A state university annual report showed that its retention rate was at 24% and university administrators would like to increase this rate. After implementing several new programs during the last two years, the university reevaluated its retention rate. What is the correct alternative hypotheses for a test to determine whether the retention rate has increased during the last two years? Question options: Ha: p>0.24 Ha: p≠0.24 Ha: p<0.24 on Identify the Type I error. A state university annual report showed that its retention rate was at 24% and university administrators would like to increase this rate. After implementing several new programs during the last two years, the university reevaluated its retention rate. Identify a Type I error in the context of this hypothesis test.Question options: The university does not conclude that retention is on the rise since the retention rate can only decrease. The university does not conclude that retention rate is increasing, but in fact the retention rate has increased from 24%. The university concludes that retention is on the rise since the retention rate can only increase. The university concludes that retention rate is increasing, but in fact it has not. on Identify the correct null and alternative hypotheses. A waste management service attempts to design routes so that each of their trucks pick-up on average four tons of garbage or less. A garbage collector believes, however, that he averages picking up more than four tons of garbage per day and decides to perform a hypothesis test. Question options: H0: µ = 4 vs. Ha: µ<4 H0: µ = 4 vs. Ha: µ >4 H0: µ = 4 vs. Ha: µ ≠ 4 on Identify the Type II error. A waste management service attempts to design routes so that each of their trucks pick-up on average four tons of garbage or less. A garbage collector believes, however, that he averages picking up more than four tons of garbage per day and decides to perform a hypothesis test. Identify a Type II error in the context of this hypothesis test. Question options: Concluding that the garbage collector picks up on average more than 4 tons of garbage per day when, in fact, he doesn’t. Not concluding that the garbage collector picks up on average more than 4 tons of garbage per day when, in fact, he does. Concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact, he picks up more.Not concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact, he does on Use the p-value method to conduct the hypothesis test. A waste management service attempts to design routes so that each of their trucks pick-up on average four tons of garbage or less. A garbage collector believes, however, that he averages picking up more than four tons of garbage per day and decides to perform a hypothesis test. If the hypothesis test is performed at a 5% significance level and the resulting pvalue is 0.04. Your conclusion should be: Question options: Fail to reject H0 because the p-value is less than 0.05. Reject H0 because the p-value is less than 0.05. Accept H0 because the p-value is less than 0.05. Fail to accept H0 because the p-value is less than 0.05. on Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t. A local newspaper reported that for the adult population of a town, the mean annual salary is $30,000. Test the claim that for the adult population of this town, the mean annual salary is greater than $30,000. Sample data are summarized as n = 17, sample mean = $22,298, and s = $14,200. Use a significance level of alpha = 0.05. Find the test statistic t. Question options: -2.24 -1.57 1.57 2.240.05 on Assume a normal distribution and use a hypothesis test to test the given claim. According to city reports, it was found that the mean age of the prison population in the city was 26 years. Marc wants to test the claim that the mean age of the prison population in his city is less than 26 years. He obtains a random sample of 25 prisoners and finds a mean age of 24.4 years and a standard deviation of 9.2 years. At a significance level of 0.05, what should his conclusion be? Note: The p-value = 0.1966. Question options: Do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years. Reject the null hypothesis. The evidence suggests that the mean age is less than 26 years. There is not enough information to perform the test. Do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 24.4 years. Reject the null hypothesis. There is sufficient evidence that the mean age is less than 24.4 years. on State your conclusion to the hypothesis test. A certain academic program claims that their students graduate in less than 4 years on average. A random sample of 50 students is taken and the mean and standard deviation are found. The test statistic is calculated to be -1.69. Using a 5% significance level, the conclusion would be: Question options: there is sufficient sample evidence for the program’s claim to be considered correct. there is insufficient sample evidence for the program’s claim to be considered correct. there is insufficient sample evidence for the program’s claim to be considered incorrect. there is sufficient sample evidence for the program’s claim to be considered incorrect. onState your conclusion to the hypothesis test. A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 22 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of n=33 wind speed recordings (taken at random intervals), the wind speed at the site averaged 22.8 mph, with a standard deviation of 4.3 mph. To determine whether the site meets the organization's requirements, perform the following hypothesis test at the 1% significance level and state your conclusion. Ho: μ = 22 HA: μ > 22 Question options: At α = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 22 mph. At α = .01, there is not sufficient evidence to conclude the true mean wind speed at the site exceeds 22 mph. We are 99% confident that the site meets the organization's requirements. We are 99% confident that the site does not meet the organization's requirements. on Assume a normal distribution and use a hypothesis test to test the given claim. A firework fuse is designed to have an average burn-time of 5 seconds before ignition. For liability reasons, the company that makes these fuses undergoes random testing to make sure that its fuses meet this standard. A random sample of 20 fuses results in an average burn-time of 5.3 seconds with a sample standard deviation of 0.7 seconds. Assuming the burn-time for an individual fuse is normally distributed, perform the appropriate hypothesis test at a 5% significance level to determine if the fuses perform according to design. Question options: There is insufficient evidence to conclude the burn time is not 5 seconds. There is sufficient evidence to conclude the burn time is greater than 5 seconds.There is sufficient evidence to conclude the burn time is less than 5 seconds. There is sufficient evidence to conclude the burn time is not 5 seconds. There is insufficient evidence to conclude the burn time is 5 seconds. on Select the most appropriate response. The level of significance, a, for a test of hypothesis represents: Question options: the probability that the test statistic will fall in the rejection region, assuming the null hypothesis is true. the acceptable probability of making a Type I error. the probability of rejecting the null hypothesis when it is in fact true. all of the above. on State your conclusion to the hypothesis test. If a 95% confidence interval for μ is calculated to be (21.4 , 27.9) , what would be the result of a hypothesis test at a 5% significance level performed on the set of hypotheses? H0: μ=27 vs H1: μ≠27 Question options: There is not enough information to test this hypothesis. The null hypothesis would be rejected. The alternative hypothesis would be rejected. The null hypothesis would not be rejected.