Final answer:
The student's questions pertain to assessing the fairness of a coin by formulating null and alternative hypotheses, selecting an appropriate distribution, calculating the test statistic, finding the p-value, and making decisions based on this process. A t-test will be performed for each data set to determine if they are significantly different from a given value, using a 5% significance level.
Step-by-step explanation:
The student's questions relate to statistical hypothesis testing, specifically testing the fairness of a coin and comparing data sets using t-tests at a 5% significance level. When discussing the fairness of a coin, we can address the question by formulating a null hypothesis (H0) and an alternative hypothesis (Ha), determining the appropriate distribution for the test, calculating the test statistic, and then using this to find the p-value and make a decision regarding the hypotheses.
For example, if Tim claims to have flipped 7 heads in a row with a fair coin, we might set H0 to be 'the coin is fair' and Ha to be 'the coin is not fair'. The random variable in this case would be the number of heads in a series of flips. Because flipping a coin is a binomial process, we would use a binomial distribution to find the probability of flipping 7 heads in a row, and hence determine the p-value. For a fair coin, the chance of flipping a head on any single toss is 0.5. The p-value for flipping 7 heads in a row would then be (0.5)^7, which is about 0.0078 or 0.78%. Since this is below the 5% significance level, we might reject the null hypothesis and consider the result suspicious, indicating the coin may not be fair.
To perform a t-test for data sets B, C, and D, the steps are similar: determine the null and alternative hypotheses for each, use the appropriate test statistic based on the sample size and variance (typically a t-score for small sample sizes), compare the calculated p-value to the significance level, and decide whether to reject the null hypothesis.