The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for less than 368 minutes. For a sample of 78 patients, the mean time the drug stayed in the system was 363 minutes. Assume the variance is known to be 529. State the null and alternative hypotheses for the above scenario
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The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for less than 368 minutes. For a sample of 78 patients, the mean time the drug stayed in the system was 363 minutes. Assume the variance is known to be 529.
State the null and alternative hypotheses for the above scenario.
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- A new fly spray is applied to 50 samples each of 5 flies and the number of living fliescounted after an hour. The results were as follows: Number living 0 1 2 3 4 5 frequency 7 20 12 9 1 1 i. Calculate the mean number of living flies per sample and hence an estimate for p, the probability of a fly surviving the sprayii. Using your estimate calculate the expected frequencies (each correct to one decimalplace) corresponding to a binomial distributioniii. Perform a chi – square goodness – of – fit test using a 5% significance level.(c)The time to deliver packaged containers by a logistics company is found fromsamples of size 4. The mean and standard deviation of delivery times is estimated tobe 140 hours and 6 hours, respectively.(a) Find the 2 sigma and 3 sigma control limits for the average delivery time.(b) Explain a type I and type II error specifically in this context.(c) If the mean delivery time shifts to 145 hours, what is the probability of notdetecting this by the second sample after the shift?(d) What is the ARL? ExplainIn a process of filling soda bottles 8% of the total is not completely filled, a potential buyer of the product decides to reject a large purchase batch yes to section a sample of 225 bottles the percentage of bottles that are not completely filled is greater than 7% with a probability greater than 85% a) Under these conditions will they buy the lot? justify the answer b) What is the minimum sample size so that the lot is not bought?