A pharmaceutical company has created a new drug to decrease how long patients suffer from a runny nose while having a cold. It is known that without treatment, on average, people report having a runny...

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Extracted text: A pharmaceutical company has created a new drug to decrease how long patients suffer from a runny nose while having a cold. It is known that without treatment, on average, people report having a runny nose for 74 hours while having a cold. A test is organised for this new drug, hoping to prove the drug indeed decreases the duration of symptoms: 196 patients use it at the first sign of a runny nose and record how long they suffer from this runny nose; on average the recorded duration is 68 hours. We suppose the observations are independent and identically distributed, and the duration of symptoms during a cold follows an exponential distribution. Thus X, ~ Erp(A), where X; is the duration of runny nose recorded by patient i, measured in hours. Assuming the null hypothesis from the last exercise holds, specify an expression for the standardised version Z of the estimator X, of u such that Z~N(0,1). Then calculate the observed value z of the test statistic, and specify the critical region at level of significance a = 0.04 Use the function section of the virtual keyboard to enter intervals. In terms of Y = X, a suitable test statistic is Z = | The observed statistic z is (to 2 decimal places) The critical region is (write an interval or union of intervals with 2 decimal places)