A drug manufacturer has an advertisement for a new drug used in the treatment of patients with irregular heartbeats. The ad states that "testing indicates that only 5% of the users of our drug will have any adverse reaction". That is, they are claiming that thepopulation proportionof users of this drug who will have an adverse reaction isp=.05.The FDA notes that this value is lower than other similar drugs that are already on the market. The FDA has asked the manufacturer to provide the results of their testing so that they can evaluate the validity of the claim used in their advertising. The manufacturer indicates that they performed a hypothesis test using the following hypotheses:Ho:p=.05andHa:p>.05. Their advertising claim was then based on the results of this test.

1. The manufacturer provided the FDA with their report which indicates that in arandom sample of 475patients with an irregular heartbeat that used the drug, thesample proportionof users who had an adverse reaction waspobs=.0737. The report then stated the following: "Although the observed sample proportion is larger than .05, we have concluded that the sample proportion DOES NOT providesufficient evidenceto conclude that thepopulation proportionof patients experiencing adverse reactions isgreater than .05. We therefore believe that our advertising claim is valid." Identify the largest value for alevel of significancethat the manufacturer could have used and still have their conclusion regarded asstatistically appropriate? (You may want to word you answer as "The level of significance that they used could not be any larger than ________." (4 decimal places)
2. The FDA has informed the manufacturer that they performed more extensive testing of the hypotheses given above. An analyst used arandom sample of 1900patients with irregular heartbeats for their analysis. The analyst reported that she observed asample proportionof users of the drug experiencing an adverse reaction to bepobs=.0653.When informed of these results, the manufacturer's response was: "Thesample proportionof patients with adverse reactions observed by the FDA issmallerthan the value we observed in our testing (.0653 vs. .0737). This indicates that their evidence in favor of the claim thatp>.05isevenweakerthan the evidence seen in our testing. This outcome further validates the claim made in our advertisement." Do youAGREE or DISAGREEwith the manufacturer's analysis that the FDA has"weaker evidence"in favor of the claim thatp>.05?
3. (4 points) The FDA analyst summarizes the results of her test as follows: "At a level of significance of=.005, we have observedsignificant evidencethat supports the claim that the population proportion of patients using this drug who will suffer an adverse reaction isgreater than .05." From a statistical standpoint, which of the following statements is TRUE?Circleyour answer. Has the analyst correctly or incorrectly interpreted the results of the sample.

The analyst hascorrectlyinterpreted the results of the sample.

The analyst hasincorrectlyinterpreted the results of her sample.