2. Suppose a researcher finds that the sample average in their sample of 25 observations is X = 8. Suppose the researcher knows that the population variance is o = 4. Use this information to answer the following questions (a) Suppose the researcher claims that the population mean u is greater than 10. Set up the null and alternative hypothesis to test this claim. (b) Can the researcher reject the null hypothesis at the 95% confidence level? (c) Suppose the researcher claims that the population mean is equal to 10. Set up the null and alternative hypothesis to test this claim. (d) Can the researcher reject the null hypothesis at the 99% confidence level? (e) Suppose the researcher wants to estimate the true mean and have a margin of error of 1 unit at a 95% confidence level. What sample size is needed to achieve this? Page 2