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 2 ID: MST.FET.HT.PHT.01.0040A [1 mark] mark] Three years ago, a referendum was held to decide on whether to pass Proposition 4815162342. Every eligible voter in the nation voted on this proposition, and it was denied. The proportion of 'yes' votes was = 0.46. Since that day, the government has released a variety of public service announcements in favour of the proposition. Today, the government believes that the proportion of 'yes' votes has increased from its figure three years ago. A hypothesis test is conducted to test this. Select the correct null and alternative hypotheses: H0: HA: = 0.46 0.46 H0: HA: = 0.46 < 0.46 H0: HA: = 0.46 0.46 H0: HA: = 0.46 0.46 H0: HA: = 0.46 = 0.46 H0: HA: = 0.46 > 0.46 2 of 2 ID: MST.FET.HT.PHT.02.0020A [1 mark] mark] A group of home-brewers have always used a particular method of brewing beer. With the same amount of ingredients each time, their brews contain an average of = 13.737 gallons of beer. The standard deviation is = 1.321 gallons. Rudy has a new and cheaper brewing method. While it is cheaper, Rudy suspects that it will decrease their productivity. The group decide to collect a sample of brewing amounts and conduct a hypothesis test on the mean amount of brew created by the new method. They will be using the value = 1.321 as their population standard deviation. The null and alternative hypotheses are set to be: H0: = 13.737 HA: < 13.737 Before they collect a sample or do the test, Sam thinks about the new brewing method. He suspects that, while it may decrease the average amount of brew created, it may actually increase it instead. Sam suggests that the alternative hypothesis should simply state that the population mean is not equal to 13.737: H0: = 13.737 HA: 13.737 Sam believes that: instead of conducting a one-tail test, they should conduct a two-tail test. instead of conducting the particular one-tail test that was proposed, they should conduct a different kind of one-tail test. instead of conducting the particular two-tail test that was proposed, they should conduct a different kind of two-tail test. instead of conducting a two-tail test, they should conduct a one-tail test. Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:04 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 3 ID: MST.FET.HT.CMHT.01.0010A [2 marks] marks] A particular characteristic is of interest to a researcher. The researcher is particularly interested in the mean value of this characteristic in the population. A hypothesis test for the mean () is to be performed. Select all the pieces of information that are needed in order to calculate the corresponding z test statistic: the actual population mean the population standard deviation the sample mean calculated the size of the sample selected the proposed population mean the level of significance used the characteristic of interest 2 of 3 ID: MST.FET.HT.CMHT.03.0010A [1 mark] mark] You may find the standard normal table useful in answering this question. Consider the hypothesis test with the following null and alternative hypotheses: H0: = 0.6 HA: < 0.6 If the level of significance used is = 0.1, the region of rejection is the set of numbers: less than -1.645 whose absolute value is greater than 1.645 whose absolute value is less than 1.28 whose absolute value is less than 1.645 less than -1.28 greater than 1.28 whose absolute value is greater than 1.28 greater than 1.645 3 of 3 ID: MST.FET.HT.CMHT.02.0020A [2 marks] marks] Painadol is a well trusted, popular pain-killer used by millions throughout the country. Recently an epidemic of headaches has hit the nation and the manufacturers of Painadol have created a new, stronger painkiller called Painadene. The manufacturers are interested in testing whether the speed of pain relief is different with Painadene. It is known that the mean time taken by Painadol tablets to relieve pain is 32 minutes and the standard deviation is 6 minutes. The manufacturers would like to construct a hypothesis test for the mean time () taken for Painadene tablets to relieve pain assuming the same population standard deviation () as the Painadol tablets. A random sample of 38 people with headaches tried the new Painadene tablets and the mean time taken to relieve the pain was calculated as 30.97 minutes. The hypotheses that will be used by the manufacturers are H0: = 32 and HA: 32. You may find this standard normal table useful throughout the following questions. a) Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer as a decimal to 3 decimal places. z= b) Using the test statistic for Painadol's hypothesis test and a level of significance of = 0.1, Painadol should the null hypothesis. Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:06 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 3 ID: MST.FET.HT.CHT.03.0020A [2 marks] marks] Gail is a student in a class that has been asked to conduct a hypothesis test for a population proportion. The null and alternative hypotheses are: H0: = 0.4 HA: 0.4 Gail is given a sample and calculates the test statistic. Using a level of significance of = 0.05, she does not reject the null hypothesis. Gail's friends, Andrew and Ben, also use the sample to calculate a test statistic. However, they differ in the level of significance they use. Andrew uses a level of significance of = 0.1, while Ben uses = 0.01. All three students perform their calculations correctly. For each of Gail's friends, select whether or not they reject the null hypothesis, or whether it is impossible to tell from the information given. Reject a) Andrew b) Ben 2 of 3 Doesn't reject Cannot tell ID: MST.FET.HT.CHT.01.0030A [1 mark] mark] April is a statistics student who has extensive computer programming skills. She programs a random-number generator that produces numbers that follow the normal distribution with mean = 19 (her favorite number) and standard deviation = 2. April's friend Augustus does not know that the population mean is 19. However he knows that April's favorite number is 19, and decides to conduct a hypothesis test with the following hypotheses: H0: = 19 HA: 19 The result of the test is that Augustus rejects the null hypothesis. Augustus has: committed a Type I error committed a Type II error not committed a Type I error or Type II error committed both a Type I error and a Type II error 3 of 3 ID: MST.FET.HT.CHT.02.0040A [3 marks] marks] Select whether the following changes to a hypothesis test will cause the value of to increase, decrease or remain unchanged. In each case, assume all other aspects of the test remain the same. Increase a) A larger level of is selected for the test. b) There is a decrease in the magnitude of the critical value(s). c) A larger sample size is selected for the test. Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:06 http://www.perdisco.com.au Decrease Unchanged 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 3 ID: MST.FET.HT.HTPP.01.0020A [3 marks] marks] The Mean Corporation would like to invest in the booming health food industry. It is considering the creation of a health-drink franchise called Goose Juice. The investment department of the Mean Corporation wants to investigate the feasibility of this venture by examining the profits of similar franchises. It believes that the venture will be feasible if an average annual profit of more than $70,000 can be expected from each Goose Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $8,600. The Mean Corporation's statisticians would like to construct a hypothesis test for the mean annual profit () earned by health-drink franchises. A random sample of 29 franchises were chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $71,650. The hypotheses that will be used by the statisticians are H0: = 70,000 and HA: > 70,000. You may find this standard normal table useful throughout the following questions. a) Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer to 3 decimal places. z= b) Using the test statistic for the Mean Corporation's hypothesis test and level = 0.05, the Mean Corporation should the null hypothesis. c) If the sample size is increased to 49 (but the sample mean remains unchanged), the Mean Corporation should 2 of 3 the null hypothesis. ID: MST.FET.HT.HTPP.02.0020A [2 marks] marks] The CEO of the Myths chip company is concerned about the net weight of chips in their 2 ounce chip bags. He decides that he wants to be fairly sure that the mean weight of these chip bags () is greater than 2 ounces. A hypothesis test is conducted with the following hypotheses: H0: = 2 HA: > 2 The level of significance used in this test is = 0.05. A random sample of 26 chip bags are collected and weighed. The sample mean weight is calculated to be x = 2.11 and the sample standard deviation is s = 0.31. You may find this Student's t distribution table useful throughout this question. a) Calculate the test statistic (t) for this test. Give your answer to 4 decimal places. t= b) The result of this test is that the null hypothesis 3 of 3 rejected. ID: MST.FET.HT.HTPP.03.0020A [2 marks] marks] The government of Preon (a small island nation) was voted in at the last election with 66% of the votes. That was 2 years ago, and ever since then the government has assumed that their approval rating has been the same. Some recent events have affected public opinion and the government suspects that their approval rating might have changed. They decide to run a hypothesis test for the proportion of people who would still vote for them. The null and alternative hypotheses are: H0: = 0.66 HA: 0.66 The level of significance used in the test is = 0.025. A random sample of 105 people are asked whether or not they would still vote for the government. The proportion of people that would is equal to 0.771. You may find this standard normal table useful throughout this question. a) Calculate the test statistic (z) for this hypothesis test. Give your answer to 3 decimal places. z= b) According to this test statistic, you should Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:06 http://www.perdisco.com.au the null hypothesis. 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.HT.PAHT.01.0010A [2 marks] marks] Geoff has been running a restaurant in the city for many years. He knows from experience that the proportion of customers that leave tips at this restaurant is 0.62. Geoff has recently opened a restaurant in a suburban area. It seems that tipping habits are different in the suburbs: Geoff believes that the proportion of customers that tip at his new restaurant ( ) may be different to 0.62. He conducts a hypothesis test to find out. The null and alternative hypotheses are: H0: = 0.62 HA: 0.62 Geoff takes a random sample of 104 customers and notes whether or not they leave a tip. In this sample, the proportion of people that leave a tip is 0.65. You may find this standard normal table useful throughout this question. a) Calculate the test statistic (z). Give your answer to 2 decimal places. z= b) Calculate the P-value. Give your answer as a decimal to 4 decimal places. P= 2 of 2 ID: MST.FET.HT.PAHT.02.0030A [3 marks] marks] A psychologist has developed an aptitude test which consists of a series of mathematical and vocabulary problems. The test was designed to result in an average score of 64.3. However, it is suspected that the true average is actually greater than this. A hypothesis test is conducted. A random sample of 40 people have taken the test and their results recorded: 90 43 70 95 58 68 70 67 83 42 59 68 80 55 67 50 79 54 94 65 47 79 52 51 61 50 88 62 64 76 94 82 88 66 81 72 55 78 67 65 Download the data You may find this Student's t distribution table useful throughout this question. a) Calculate the test statistic (t) for the hypothesis test. Give your answer to 4 decimal places. t= b) A level of significance of = 0.1 is to be used for the test. The P-value for this test statistic is than the level of significance. c) The result of this test is that the null hypothesis is Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 04, 2016, 21:07 http://www.perdisco.com.au