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.01.0020A [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 50.65, with a population standard deviation of 10.61. For advanced students, the population mean score in the test is 81.40, with a population standard deviation of 15.56. 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 50 general-level students and a sample of 200 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 0.2 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 20 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 19.87 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 19.87 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.03.0020A [1 mark] mark] The number of diners at a restaurant each day is recorded and a daily average is calculated every month (assume 30 days in a month). The number of diners each day has a mean of 110 and a standard deviation of 54, but does not necessarily follow a normal distribution. The probability that a daily average over a given month is greater than x is 2.5%. Calculate x. You may find standard normal table useful. Give your answer to 3 decimal places. x= Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Saturday, April 30, 2016, 09:11 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.01.0010A [1 mark] mark] A city has 1,158,143 residents. A recent census showed that 321,476 of these residents regularly use the city's public transportation system. A survey is being conducted in which 1,109 of the city's 1,158,143 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 mean of this distribution. Give your answer to 2 decimal places. Mean = 2 of 2 ID: MST.FET.SD.SDP.02.0030A [1 mark] mark] The government regulator of the insurance industry requires that all insurers have less than 14% of their reserves invested in high risk assets. A high risk asset is defined by the regulator as one which has an expected return greater than 24.41% pa. The regulator has selected IHI Insurance for a surprise evaluation. The population proportion of IHI reserves that are invested in high risk assets is equal to 0.2. However the regulator will not check all of the reserves so IHI has hope that it might still pass the evaluation. The regulator has randomly selected 55 of the IHI reserve investments and will test whether each one is a high risk asset. Calculate the probability that IHI passes the evaluation based on the sample proportion of reserve investments. You may find this standard normal table useful. Give your answer as a decimal to 4 decimal places. (Hint). probability = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Saturday, April 30, 2016, 09:12 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.01.0020A [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 35% of the community support the law. You decide to survey 100 people, and find that 40% of this survey support the law. a) Based on the assumption that the population proportion is 35%, 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 right of this z-score. That is, determine the area to the right 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 35%. B: If your colleague is correct and the true population proportion is 35%, then x% of all samples will produce a sample proportion of 40% or lower. C: If your colleague is correct and the true population proportion is 35%, then x% of all samples will produce a sample proportion of 40% or higher. D: There is a chance of x% that the true population proportion is 35% or lower. E: There is a chance of x% that the true population proportion is 35% 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.02.0040A [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 859. 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 38. You randomly select 44 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 859, then for 95% of all samples of size n = 44, the sample mean will be somewhere between and cars. b) Over the 44 days, you find that an average of 866 cars pass through the intersection. Therefore with 95% 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 | Saturday, April 30, 2016, 09:12 http://www.perdisco.com.au