Steps in Hypothesis Testing: Videos & Practice Problems

In a survey conducted by a health magazine, $1050$ people were asked if they support the use of artificial intelligence in diagnosing diseases. $567$ of the respondents (or $54\%$) said they were in favor. A health expert argues that the public's support is not genuinely in favor, suggesting that the responses might as well be random, similar to flipping a coin. The probabilities for the survey data are given as:

• $P\left(A\right)=0.5$, the probability that a respondent supports AI diagnosis,
• $P\left(B\right)=0.0005$, the probability of exactly $567$ out of $1050$ support AI diagnosis,
• $P\left(C\right)=0.004$, the probability of $567$ or more out of $1050$ support AI diagnosis.

Is the support of $567$ respondents significantly high to refute the health expert's claim?