Final answer:
In the Metcalfe and Wiebe experiment, confidence ratings on 'nearness to a solution' increase over time prior to the solution of an insight problem. To raise confidence levels in a survey while maintaining the error bound, a larger sample size is needed. Additionally, higher confidence levels often result in a wider confidence interval.
Step-by-step explanation:
In the Metcalfe and Wiebe experiment, confidence ratings on "nearness to a solution" typically increase over time prior to the solution of an insight problem. This phenomenon is connected to the sudden 'aha' moment often reported by individuals when they solve a problem that requires insight. These confidence ratings reflect a subjective feeling that one is getting closer to the solution, even though the person may not be consciously aware of the solution until it suddenly becomes apparent.
If a firm wished to increase its level of confidence and keep the error bound the same by taking another survey, it should increase the sample size. However, if the firm conducted another survey and only surveyed 49 people while keeping the error bound the same, the level of confidence would decrease. This is because a smaller sample size increases the margin of error and thus reduces the confidence level associated with the survey's results.
The confidence interval and its relationship with the level of confidence revolve around the idea that as the confidence level increases, the width of the confidence interval typically increases. This is because to be more confident that you have captured the true population parameter, you must accept a wider range of potential values.