If the alpha level changed from a=0.05 to a=0.01, what happens to the critical region and ehat happens to the probability of type 1 error
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- If the alpha level is changed from a = .OS to a = .01 What happens to the boundaries for the critical region? What happens to the probability of a Type I error?If the alpha level is changed from a = 0.05 to a = 0.01, what happens to the critical region and what happens to the probability of a Type I error?What is the critical value for a right-tailed t test when alpha = 0.025 and n = 13? Explain.
- The population standard deviation is known, the α=0.01 in a left tailed testThe critical value for the rejection region is Zc=Left ventricular mass (LVM) is an important risk factor for subsequentcardiovascular disease. A study is conducted to assess the relationship between the size of LVM in children (as determined from an echocardiogram) and the size of LVM four years later in the same individuals. Does LVM change over time in children? Completely conduct the appropriate hypothesis and list any additional necessary assumptions (you can assume that additional assumptions are met by the data) test with alpha =0.01. i Baseline LVM LVM 4 years later 1 134 126 2 86 142 3 78 111 4 73 82You are performing a two-tailed z-test If a = 0.2, find the positive critical value, to two decimal places.
- As the alpha level gets lower, which error rate also gets lower? Type I Type IIThe most common test for osteoporosis (low bone density) is a bone density scan by a DEXA test (dual- energy X-ray absorptiometry). The bone density of a population is normally distributed. A woman has the test and finds that she has a bone density of 932 grams per square centimeter, which puts her at a density where approximately 12% of the population has bone density less than hers. In the population of women her age, the mean bone density is 956 grams per square centimeter. What is the standard deviation for the bone density? 22.If a Type II error is considered more serious in a certain situation, would you choose a high or low alpha value? Explain.
- An analogue signal received at a detector, measured in microvolts, is normally distributed with mean of 185 and variance of 244. What is the probability that is the signal will be less than 203 µV given that it is less than 184 µV?Let Y be a random variable with the mgfM(t) = .35e^(−4t) + .1 + .25e^(2t) + .3e^(4t).(a) What is the pmf of Y?(b) Calculate the variance of Y directly from the pmf you determined in part (a).(c) Calculate E[Y^4] directly from the mgf.A proton emitter produces proton beams with changing kinetic energy that is uniformly distributed between three and eight joules. Suppose that it is possible to adjust the upper limit of the kinetic energy (currently set to eight joules). • What is the mean kinetic energy? What is the variance of the kinetic energy? What is the probability that a proton beam has a kinetic energy of exactly 3.5 joules? a. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a continuous distribution O b. E(X) = 5, V(X) = 1.33, probability is zero (0) because X has a uniform distribution O c. NONE O d. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a uniform distribution