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 the population proportion of users of this drug who will have an adverse reaction is p=.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: :=. and :>. Their advertising claim was then based on the results of this test.

a) The manufacturer provided the FDA with their report which indicates that in a random sample of 475 patients with an irregular heartbeat that used the drug, the sample proportion of users who had an adverse reaction was P hat observed=.. The report then stated the following: "Although the observed sample proportion is larger than .05, we have concluded that the sample proportion DOES NOT provide sufficient evidence to conclude that the population proportion of patients experiencing adverse reactions is greater than .05. We therefore believe that our advertising claim is valid." Identify the largest value for a level of significance that the manufacturer could have used and still have their conclusion regarded as statistically appropriate? (You may want to word you answer as "The level of significance that they used could not be any larger than ________" round to 4 decimal places.