Hypothesis Testing a) You would like to lower the probability of a Type ll error
ID: 3151882 • Letter: H
Question
Hypothesis Testing
a) You would like to lower the probability of a Type ll error without increasing the probability of committing a Type l error. How can you accomplish this?
b) Suppose that you are given the 95% confidence interval for a parameter i. Is the following statement true or false?
The probability that the true value of i is included in the interval is 0.95. Explain/Justify your answer.
c) If x has a standard normal distribution, what is the distribution of x2?
d) If x has variance x2 and y variance y2, and their covariance is xy, what is the variance of x+y?
e) If x and y in part d above have a normal distribution with mean x and y, respectively, write the test statistic for the sum x+y when the null hypothesis is that x+y=0. What is the distribution of the test statistic?
Explanation / Answer
a) You would like to lower the probability of a Type ll error without increasing the probability of committing a Type l error. How can you accomplish this?
You can do this by increasing your sample size. [ANSWER]
b) Suppose that you are given the 95% confidence interval for a parameter i. Is the following statement true or false?
The probability that the true value of i is included in the interval is 0.95. Explain/Justify your answer.
FALSE. The true value of i is only either inside or outside the interval, and we cannot measure its probability. Rather, the correct interpretation is that 95% of intervals using this method of constructing the confidence interval contains the true value of i. [ANSWER, FALSE]
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