ductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.SD.SDM.01.0010A [3 marks] marks] A company provides tuition for mathematics students across the country. It provides two levels of tuition: tuition for general-level students and tuition for advanced-level students. All students who receive tuition at this company must first complete a test, to assess their initial comprehension of mathematics. For general-level students, the population mean score in this test is 49.75, with a population standard deviation of 16.26. For advanced students, the population mean score in the test is 81.86, with a population standard deviation of 11.60. A statistician wants to study the results of a random selection of general students and a random selection of advanced students. The statistician intends to draw a sample of 200 general-level students and a sample of 50 advanced-level students. a) From the following list, select the statements that are true. For each statement, assume that all other measures remain constant in that instance. The larger a population mean, the greater the variation in sample means for samples from that population. The smaller a population mean, the greater the variation in sample means for samples from that population. The larger a population variance, the greater the variation in sample means for samples from that population. The smaller a population variance, the greater the variation in sample means for samples from that population. The larger the sample size for samples from a population, the greater the variation in sample means. The smaller the sample size for samples from a population, the greater the variation in sample means. b) For the samples described in the scenario above, the sample mean scores for samples of general-level students will have a level of variation than the variation in sample mean scores for samples of advanced-level students. 2 of 3 ID: MST.FET.SD.SDM.02.0010A [1 mark] mark] During its manufacturing process, Fantra fills its 20 fl oz bottles using an automated filling machine. This machine is not perfect and will not always fill each bottle with exactly 20 fl oz of soft drink. The amount of soft drink poured into each bottle follows a normal distribution with mean 20 fl oz and standard deviation 0.17 fl oz. The Fantra quality testing department has just carried out a routine check on the average amount of soft drink poured into each bottle. A sample of 25 bottles were randomly selected and the amount of soft drink in each bottle was measured. The mean amount of soft drink in each bottle was calculated to be 19.91 fl oz. The Fantra Chief Executive Officer believes that such a low mean is not possible and a mistake must have been made. Calculate the probability of obtaining a sample mean below 19.91 fl oz. You may find this standard normal table useful. Give your answer as a decimal to 4 decimal places. p= 3 of 3 ID: MST.FET.SD.SDM.03.0030A [1 mark] mark] A particular population has a mean of 178 and a variance of 1,240. Considering the sampling distribution of sample means of all samples of size 27, calculate the value of the sample mean for which 80% of samples have a sample mean less than this value. You may find this standard normal table useful. Give your answer to 1 decimal place. Sample mean = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:00 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 2 ID: MST.FET.SD.SDP.01.0020A [1 mark] mark] A city has 1,130,816 residents. A recent census showed that 356,757 of these residents regularly use the city's public transportation system. A survey is being conducted in which 1,195 of the city's 1,130,816 residents will be randomly selected. This question relates to the proportion of the survey that is made up of people that do use the city's public transport. The proportion of people in the survey that do use public transport approximately follows a normal distribution. Calculate the standard deviation of this distribution. Give your answer to 4 decimal places. Standard deviation = 2 of 2 ID: MST.FET.SD.SDP.02.0050A [1 mark] mark] A jury is to be selected for a proceeding in which the accused is alleged to have stolen money from a business partner. According to existing data, 44% of potential jurors have been a victim of a major theft at some point in their life that will make them unfairly prejudicial against the accused. If 48 jurors are randomly chosen, calculate the probability that at least half of them will be unfairly prejudicial in this way assuming that the distribution of sample proportions is normal. You may find this standard normal table useful. Give your answer as a decimal to 5 decimal places. Probability = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:01 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 2 ID: MST.FET.SD.SDI.01.0010A [3 marks] marks] You work for a lobby group that is trying to convince the government to pass a new law. Before embarking on this, your lobby group would like to know as much as possible about the level of community support for the new law. Your colleague, based on his research into community opinion on related matters, proposes that 33% of the community support the law. You decide to survey 100 people, and find that 26% of this survey support the law. a) Based on the assumption that the population proportion is 33%, calculate the z-score of the sample proportion in your survey. Give your answer as a decimal to 2 decimal places. z= b) Determine the proportion of the standard normal distribution that lies to the left of this z-score. That is, determine the area to the left of this z-score in the standard normal distribution. You may find this standard normal table useful. Give your answer as a percentage to 2 decimal places. Area = % c) Denote by x% the percentage proportion you calculated in part b). Consider the following five potential conclusions: A: There is a chance of x% that your friend is correct, that the true population proportion is 33%. B: If your colleague is correct and the true population proportion is 33%, then x% of all samples will produce a sample proportion of 26% or lower. C: If your colleague is correct and the true population proportion is 33%, then x% of all samples will produce a sample proportion of 26% or higher. D: There is a chance of x% that the true population proportion is 33% or lower. E: There is a chance of x% that the true population proportion is 33% or higher. Select the statement that can be inferred from your findings: A B C D E 2 of 2 ID: MST.FET.SD.SDI.02.0030A [3 marks] marks] You work on a traffic management team for the city. There has been a proposal to add a new lane to a road near a busy intersection. As part of the research into whether or not to build the new lane, the team would like to know how many cars, on average, pass through this intersection at peak hour each day (5 pm to 6 pm). Your colleague has developed the hypothesis that the population mean is 899. You intend to test this hypothesis. For the purposes of this research, the team is assuming that the standard deviation in the number of cars passing through each hour is 39. You randomly select 50 days on which to monitor the traffic going through this intersection. a) Complete the following statement by filling in the correct numbers. Give your answers to the nearest whole number of cars. If the true population mean really is 899, then for 90% of all samples of size n = 50, the sample mean will be somewhere between and cars. b) Over the 50 days, you find that an average of 911 cars pass through the intersection. Therefore with 90% confidence you can rule out the possibility that your colleague's hypothesis was correct cannot rule out the possibility that your colleague's hypothesis was correct Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:01 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 2 ID: MST.FET.E.PE.01.0020A [1 mark] mark] A 91% confidence interval for the mean has been calculated using a sample size of 24. If the sample size is decreased then, all other things remaining constant, the confidence interval will become 2 of 2 . ID: MST.FET.E.PE.02.0040A [1 mark] mark] All statistical estimates inherently involve some level of imprecision and some level of uncertainty. Beth has collected a sample from a numerical variable X. She has calculated a sample mean of 6,139. From this, Beth draws the following inference: 'I am 95% confident that the population mean of X is somewhere between 6,080 and 6,198.' In this inference, Beth has: failed to acknowledge both the imprecision and uncertainty in statistical estimates acknowledged both the imprecision and the uncertainty in statistical estimates acknowledged the imprecision but failed to acknowledge the uncertainty in statistical estimates acknowledged the uncertainty but failed to acknowledge the imprecision in statistical estimates Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:02 http://www.perdisco.com.au