Final Answer:
a. 98% CI for mean movie ticket price: $11.01 to $11.77.
b. Margin of error: $0.38.
c. Confidence level: 98%.
d. Population parameter: Mean movie ticket price.
Explanation:
In statistical analysis, a 98% confidence interval was calculated to estimate the mean movie ticket price. The interval, ranging from $11.01 to $11.77, indicates that we are 98% confident that the true mean falls within this range. This means that if we were to take numerous samples and create intervals in the same manner, we would expect about 98% of them to contain the actual population mean. The margin of error, which is $0.38, represents the range within which we expect the sample mean to deviate from the population mean.
The confidence level of 98% signifies the degree of certainty in our interval estimate. In practical terms, it implies that if this study were repeated many times, 98% of the resulting confidence intervals would encompass the true population mean. This high confidence level is often chosen in scenarios where precision is crucial. It reflects a balance between being reasonably certain about our estimate while still allowing for some variability.
The population parameter being estimated in this context is the mean movie ticket price. This parameter serves as a representative measure for the entire population of theaters under consideration. The confidence interval provides a range within which we can reasonably expect this population mean to lie based on the sample data.