A large electronics company claims that the defect rate for its flagship smartphone model is $50\%$ or less after the first year of use. A consumer advocacy group suspects the actual defect rate is different from $50\%$. The group surveys a random sample of $550$ owners who have had the phone for over a year. Of these owners, $245$ reported experiencing a major hardware defect. Determine the $P$-value for a two-tailed hypothesis test to check if the true proportion of defective phones is significantly different from $0.50$.