True or false. Determine if the following statements are true or false, and explain your reasoning. If false, state how it could be corrected.
(a) If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval.
(b) Decreasing the significance level (a) will increase the probability of making a Type 1 Error.
(c) Suppose the null hypothesis is µ = 5 and we fail to reject H0. Under this scenario, the true population mean is 5.
(d) If the alternative hypothesis is true, then the probability of making a Type 2 Error and the power of a test add up to 1.
(e) With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size , will be identified as statistically significant.