Final answer:
The question asks to find the 95% confidence limits for a coin flip scenario, but insufficient data is available to answer it directly. Instead, an explanation for testing the fairness of a coin using a chi-square test is provided.
Step-by-step explanation:
The question asks to find the 95% confidence limits for the proportion of heads when flipping a coin seven times, yielding six heads out of seven flips. To calculate this, we would typically use the formula for a confidence interval for a binomial proportion. However, the question does not provide enough information since we would need to know the standard deviation or be able to assume a normal distribution to approximate the confidence interval for such a small number of trials.
Instead, I can demonstrate a similar process using an example. For a coin flipped 100 times with known outcomes of HH, HT, TH, and TT, we could test the fairness of the coin at the 5 percent significance level by determining if the observed results significantly deviate from the expected results of a fair coin. This would involve a chi-square test for goodness-of-fit. The expected frequency for each outcome, assuming a fair coin, is 25 HH, 25 HT, 25 TH, and 25 TT. We would then calculate the chi-square statistic and compare it to a critical value from the chi-square distribution table to make our conclusion about the fairness of the coin.