A manufacturer of a new nicotine nasal spray claims that their product has a 60% success rate for smoking cessation. In a clinical study involving 280 smokers, 125 of them quit smoking. Test the hypothesis that the success rate claimed by the manufacturer is valid at the 5% significance level.

Solve this problem on paper or a tablet and submit your work in PDF format. You must follow the rules below in your solution:

1. Your solution cannot include any R code as a solution,
2. Must include formulas, numeric setup for all intermediate calculations,
3. You must show how you obtained the Critical and Calculated values using formulas (show setup),
4. Must include a written null and alternate hypotheses (no mathematical notations here),
5. You must include a conclusion and an interpretation for your conclusion.