Final answer:
To create a 95% confidence interval for the true mean of all football fans, you need the sample size that is missing from the information provided. The interval would be calculated using the point estimate, the standard error, and the appropriate t-score for the confidence level.
Step-by-step explanation:
The student asked to find a 95% confidence interval for the true mean of all football fans based on a sample mean of $75 and sample standard deviation of $20 with a sample size of n - 49. To construct the confidence interval, we need to know the exact sample size (n), which is not provided in the information given.
However, assuming 'n-49' implies that there's a typo and 'n' is actually provided, we can estimate the interval using the t-distribution if 'n' is small or the normal distribution if 'n' is large.
To begin, we identify the point estimate of the mean (X), which is $75. Next, we calculate the standard error (SE) using the formula SE = s / √n, where 's' is the sample standard deviation ($20) and 'n' is the sample size. With the SE, we then find the t-score that corresponds to our confidence level (95%).
The confidence interval is then calculated by taking the point estimate and adding and subtracting the product of the t-score and SE. Without the exact 'n', we cannot calculate the exact interval, but this provides the general process.
The complete question is: Money spend by n-49 randomly selected football fans at a single game yields a sample mean $75 and s-$20. Find a 95% confidence interval for the true mean of all football fans is: