Can anyone helppp me solve this one? Pls? Could u write the answers on a paper so that I will clearly get the proper solution. Thank you in advance!!

1. When is it appropriate to use the t-distribution in testing a hypothesis about a population mean? 2. In what ways are the distributions of the z-statistic and the t-statistic alike? How do they differ? . Calculate the t-statistic for each of the following: a. H = 12, X = 15, s = 4, n = 12 b. H = 10, X =7.8, s = 5.1, n = 10 C. H = 5.3, X = 5, s = 0.14, n = 8 d. u = 9.1, X= 7.2, s = 1.8, n = 15 e. H = 7, X = 5, s = 3, n = 10 4. A random sample of ten measurements were obtained from a normally distributed population with mean u =6.5. The sample values are X =4.2 and s = 2. a. Test the null hypothesis that the mean of the population against the alternative hypothesis, H = 6.5. Use a = 0.05. b. Test the null hypothesis that the mean of the population against the alternative hypothesis, u * 6.5. Use a = 0.05 5. Conduct a t-test for the null hypothesis H.: u = 100 against the alternative hypothesis H: u > 100 based on 15 random observations. The sample mean is 110 and the sample standard deviation is 8. Use a = 0.05