Suppose we set the criterion for the rejection of the null that is extremely stringent, assuring us that the null will be definitely rejected. Then, which of the following is/are true?
Answer(s): D
A Type I error refers to the event that we will reject the null when, in fact, it is true. If the criterion is so stringent that you always reject the null, then the probability of type I error is one. A Type II error refers to the event that we will fail to reject the null when, in fact, it is false. If you always reject the null, then the probability of type II error is clearly zero. Also remember that the significance level is the same as the probability of making a Type I error. Hence, in this case, the significance level equals 100%.
Which of the following is/are true about a normal distribution?
Answer(s): B
A normal distribution is completely characterized by 2 parameters, mean and variance. It ranges from negative infinity to positive infinity, has a single mode or peak (occurring at the mean), is symmetrical about the mean and has zero skewness.
Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English, C. History and English are 5 credit hour courses, Statistics a 4 credit hour course and Spanish a 3 credit hour course. If 4 grade points are assigned for an A, 3 for a B and 2 for a C, what is the weighted mean for the semester grade?
The student has taken 17 credit hours. The weighted grades for each are: History:5*3 = 15. English: 5*2 = 10.Statistics: 4*4 = 16. Spanish: 3*2 = 6. Adding we have 15 + 10 + 16 + 6 = 47. Mean = 47/17 = 2.76
Suppose that you write an investment newsletter. You track 12 stocks, and you classify these stocks into equal- sized categories of buy, sell, and hold. How many different ways can you classify these stocks into thosecategories?
To answer this question, we need the formula for permutations that takes into account different ways to label things. The number of ways that you can arrange n objects so that there are n_1 of one kind, n_2 of another kind, and so on, up to n_k of a kth kind, is found by using the multinomial formula: n! /[(n_1)! * (n_2)! * ... * (n_k)!]. In this case, your equally-sized categories will be 4 of each kind, 12 in all. 12! / (4!*4!*4!) = 34,650.
A random variable with a mean equal to 2.5 and a standard deviation of 2.0 has a coefficient of variation equal to ________.
Answer(s): E
The coefficient of variation equals the ratio of the standard deviation to the mean.
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