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UESTION 4 State the point estimates used and frame the appropriate hypothesis statement of the following problems:- (a) The drug Prevnar is a vaccine meant to prevent meningitis. In clinical trials, the vaccine was given to 710 randomly selected children 12 15 months in age. Of these, 121 experienced appetite loss as a side effect. Is this signicant evidence that more than 15% of all children that take Prcvnar will have loss of appetite as a side effect? Test the relevant hypotheses at the o = 0.10 level. (2 marks) (b) In October 2000, the results of a large survey showed that 84.9% of 12460 males and 88.1 % of 12678 females had graduated from high school. Does this study support that claim that females were more likely to graduate 'om high school than males in 2000? (2 marks) (c) A study was conducted to see if putting duct tape over a wart worked better than traditional treatments. Of 104 subjects that used duct tape, 84.6% were \"healed\". Of 100 subjects using traditional treatments, 60% were \"healed\". Do these samples signicantly support that duct tape works better? (2 marks) (d) The posted speed limit on a certain residential road is 30mph. The residents believe that drivers are speeding on this road on average. They observe 20 randomly selected drivers on this road and find the mean speed to be 31.8mph with a stande deviation of 4.2mph. Is the residents' belief accurate? (2 marks) QUESTION 5 An Operation Manager claims that the cycle time to complete a fabrication process is less than 38 minutes. The Operation Manager had collected 18 cycle time data, the 18 data gives the average cycle time of 35 minutes with standard deviation of 12.2 minutes. Assumes data is normally distributed. (a) Develop the null and alternate hypotheses for the Operation Manager's claim. (2 marks) (b) At signicance level of 0. 10, what is the critical value and decision rule for the hypotheses test? (3 marks) (0) Is there evidence to doubt the Operation manager's claim at a significance level of 0.10? (5 marks) QUESIIQEJ A sweet shop sells chocolate which appear, at rst sight. to be identical. The chocolates are all in the shape of circular disks and the diameter, in millimetres with mean 275m. The sample of 19 chocolates were taken and found the diameters are as follows. 279 263 284 277 281 269 266 271262 275 266 272 281 274 279 277 267 269 275 (a) State any necessary assumptions. (1 mark) (b) Test the claims that mean diameter is 275 mm at 10% signicant level (i) State the test hypotheses. (1 mark) (ii) State the test statistic and draw the rejection/critical region. (4 marks) (iii) What is your conclusion based on (ii). (2 marks) (c) What changes would happen to your test if it is known that the standard deviation of the diameter was 5 mm? (2 marks) QUESTION 2 A research rm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. They found the distribution of amounts spent per week followed the normal distribution with a standard deviation of $5. A sample of 49 steady smokers revealed that J? = 20 (i) What is the point estimate of population mean? Explain what it indicates. (3marks) (ii) Using the 95 % level of condence, determine the condence interval for u. Explain what it indicates. (4+3 marks) QUESTION 3 A manufacturer conducted a survey among 500 randomly selected target market households in the test market for its new disposable diapers. The objective of the survey was to determine the market share for its new brand. If the sample point estimate for market share is 15%, develop a 90% condence interval. (Hint: Sample point estimation :3 = 15% =0.15 is given) (2 Marks)