Case Study 4: A car dealer wishes to learn whether they can predict customers preferred car make type based on suburb so that they could distribute their mail advertising more effectively. The table below shows the number of people in a random sample of 245 and their current cars. Suburb Nedlands Como Bentley Benz 20 15 BMW 30 20 15 Toyota 10 15 20 Hyundai 5 8 40 Kia 7 30 Your Tasks: Conduct an appropriate test to see if there is sufficient evidence to establish a connection between suburb and car preference at the 1% level of significance. Car Preference
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A car dealer wishes to learn whether they can predict customers preferred car make type
based on suburb so that they could distribute their mail advertising more effectively. The
table below shows the number of people in a random sample of 245 and their current cars.
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- Section 9.1 Question #4 Since an instant replay system for tennis was introduced at a major tournament, men challenged 1386 referee calls, with the result that 429 of the calls were overturned. Women challenged 758 referee calls, and 212 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis test? A. H0: p1=p2 H1: p1 ≠ p2 B. H0: p1 ≥ p2 H1: p1 ≠ p2 C. H0: p1 ≤ p2 H1: p1 ≠ p2 D. H0: p1 ≠ p2 H1: p1 = p2 E. H0: p1 = p2 H1: p1 > p2 F. H0: p1=p2 H1: p1 < p2 Identify the test statistic. z= ____________ (Round to two decimal…Question 16 In a test of the effectiveness of a new battery design, 16 battery-powered music boxes are randomly provided with either the old design or the new version. Hours of playing time before battery failure were as follows: New battery type (hrs) 3.3 6.4 3.9 5.4 5.1 4.6 4.9 7.2 Old battery type (hrs) 4.2 2.9 4.5 4.9 5.0 5.1 3.2 4.0 Assuming normal populations with equal variances. The null and alternative hypotheses are used to determine whether the new battery could be better than the old design. At 1% level of significance, do reject or fail to reject H0? Reject H0 because t- statistic lies between -2.625 and 2.625 Reject H0 because z-statistic lies bewteen -2.625 and 2.625 Fail to reject H0 because t-statistic is greater than 2.625 Fail to reject H0 because t-statistic is less than 2.625Question 10 In a test of the effectiveness of a new battery design, 16 battery-powered music boxes are randomly provided with either the old design or the new version. Hours of playing time before battery failure were as follows: New battery type (hrs) 3.3 6.4 3.9 5.4 5.1 4.6 4.9 7.2 Old battery type (hrs) 4.2 2.9 4.5 4.9 5.0 5.1 3.2 4.0 Assuming normal populations with equal variances. The null and alternative hypotheses are used to determine whether the new battery could be better than the old design. Compute the value of the test statistic, 1.6413 -1.6413 1.6414 -1.6414
- A report describes a survey of 500 licensed drivers. Each driver in the sample was asked if they would prefer to keep complete control of the car while driving, to use a partially self-driving car that allowed partial driver control, or to turn full control over to a driverless car. Suppose that it is reasonable to regard this sample as a random sample of licensed drivers in the United States, and that you want to use the data from this survey to decide if there is evidence that fewer than half of all licensed drivers in the United States prefer to keep complete control of the car while driving. (d) The actual sample proportion observed in the study was p̂ = 0.44. Based on this sample proportion, is there convincing evidence that fewer than 50% of licensed drivers prefer to keep complete control of the car when driving, or is the sample proportion consistent with what you would expect to see when the null hypothesis is true? Support your answer with a probability calculation. (Round…Question 7 In a test of the effectiveness of a new battery design, 16 battery-powered music boxes are randomly provided with either the old design or the new version. Hours of playing time before battery failure were as follows: New battery type (hrs) 3.3 6.4 3.9 5.4 5.1 4.6 4.9 7.2 Old battery type (hrs) 4.2 2.9 4.5 4.9 5.0 5.1 3.2 4.0 Assuming normal populations with equal variances. The null and alternative hypotheses are used to determine whether the new battery could be better than the old design. At 1%% level of significance, find the critical value (s).QUESTION 4 Titus Company, a recycling computer company ordered computer components from two differentsuppliers, namely Supplier A and Supplier B. Since Covid-19 outbreak in Malaysia, the companyhas financial constraint and need to identify which supplier has more reliable component. Duringassembly process, the number of defective components is recorded. The number of defectivecomponents for each supplier from 12 random days in a month is given in Table 3. Assume thatthe data are normally distributed and the two population standard deviations are not equal.Table 3Day 1 2 3 4 5 6 7 8 9 10 11 12Supplier A 34 36 40 39 30 38 37 39 35 41 40 38Supplier B 40 40 38 39 37 35 42 41 40 41 33 39(i) Construct a 90% confidence interval for the difference in the true average number of defectivecomponents between both suppliers.(ii) Interpret the parameter estimate obtained in (i)?(iii) What is the effect on…
- Question 6A multinational corporation is conducting a study to see how its employees in five different countries respond to three gifts in an incentivescheme. The numbers of employees who choose each of the three gifts(G1 to G3) in each of the five countries (A to E) are given in the tablein ‘Dataset6’ in the Excel document.1. Set up the structure of an appropriate statistical test to determine whether the data supports a link between choice of gift andcountry, including the statistic to be used.2. Carry out this test, showing clearly in your work how the expectedvalues are calculated for your test statistic. G1 G2 G3 A 5 17 19 B 8 20 19 C 11 16 25 D 12 19 30 E 13 20 28SCENARIO 7 Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. Use a level of significance of 0.10. Northeast South West Central 16.3 16.9 16.4 16.2 16.1 16.5 16.5 16.6 16.4 16.4 23.0 16.5 16.5 16.2 20.2 16.4 Question 45 Listen Which test are you running? Question 45 options: ANOVA Chi-Square Goodness of Fit One mean t-test One-mean z-test Question 46 Listen What is the null hypothesis? Question 46 options: Ho:The mean ages for teenagers obtaining their drivers licenses…A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1 2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. MaleDriver FemaleDriver 1.4 -0.2 1.2 0.5 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use ?males − ?females. Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to three decimal places.) t = df =…
- This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using the drug. It is hypothesized that regular exercise might help reduce the headaches. If a random sample of 205 patients using diltiazem exercised regularly and only 15 had headaches, would this indicate a reduction in the population proportion of patients having headaches? Use a 1% level of significance. 1. What is the value of the sample test statistic? (Round your answers to two decimal places.) 2. Find the P-value of the test statistic. (Round your answers to four decimal places.)This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using the drug. It is hypothesized that regular exercise might help reduce the headaches. If a random sample of 205 patients using diltiazem exercised regularly and only 18 had headaches, would this indicate a reduction in the population proportion of patients having headaches? Use a 1% level of significance. A-What is the value of the sample test statistic? (Round your answers to two decimal places.) B- Find the P-value of the test statistic. (Round your answers to four decimal places.)Reviewers from the Oregon Evidence-Based Practice Center at the Oregon Health and Science University investigated the effectiveness of prescription drugs in assisting people to fall asleep and stay asleep (source: S. Carson, M.S. McDonagh, et al., “Drug class review: Newer drugs for insomnia,” Oregon Health and Science University, 2008, http://www.ncbi.nlm.nih.gov). Suppose a study of two drugs, Sonata and Ambien, was conducted and the resulting data are contained in a file titled Shuteye. The samples reflect an experiment in which individuals were randomly given the two brands of pills on separate evenings. Their time spent sleeping was recorded for each of the brands of sleeping pills. (A) Does the experiment seem to have dependent or independent samples? Explain your reasoning. (B) Do the data indicate that there is a statistical difference in the mean time spent sleeping for people using the two drugs? Test using alpha = 0.02. Conduct a statistical procedure to determine this. (C)…