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Free CFA-Level-I Exam Braindumps (page: 295)

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A light bulb manufacturer would like to supply only those bulbs which have a life of 2,000 hours or more. Otherwise, it wants the bulbs to be rejected at the assembly line. The statistician hired by the bulb manufacturer is trying to frame the situation as a hypothesis testing problem. He should specify the null and alternate hypothesis as:

  1. Ho: average life < 2,000; H1: average life > 2,000
  2. Ho: average life = 2,000; H1: average life > 2,000
  3. Ho: average life = 2,000; H1: average life < 2,000
  4. Ho: average life >= 2,000; H1: average life < 2,000

Answer(s): D

Explanation:

In any experiment, you have a natural candidate for a default hypothesis that is maintained to be true until there is sufficient evidence to reject it. This is the hypothesis that must be selected as the null. Inthe present example, the manufacturer is in the business of supplying bulbs which have an average life of more than 2000 hours. So it is logical to assume that the processes usually produce such bulbs and occasionally produce faulty bulbs which have a shorter average life. Hence, the null hypothesis must be that any given bulb has an average life of more than 2000 hours and the alternative hypothesis must be the complement (i.e. average life is less than 2000 hours).



The larger the critical value on the z-statistic,

  1. all of these answers can happen, depending on the R-square.
  2. the harder it is to reject the null hypothesis.
  3. the easier it is to accept the null hypothesis.
  4. the easier it is to reject the null hypothesis.
  5. none of these answers.

Answer(s): B

Explanation:

To reject a null hypothesis, the z-statistic must be larger in magnitude than the critical value for a given level of significance.



If a distribution is right skewed, which of the following is/are true?

  1. It cannot be normally distributed.
    II. Its skewness is negative.
    III. It has a positive mean.
    IV. Large positive deviations dominate large negative deviations.
  2. I only
  3. I & IV
  4. II only
  5. I & III
  6. III only
  7. I, II, III & IV

Answer(s): B

Explanation:

A normal distribution is symmetrical and hence, has zero skewness i.e. it is neither positively nor negatively skewed. If the distribution is right skewed, its skewness is positive but it does not necessarily have a positive mean.



Which of the following statements is false in reference to confidence intervals and/or tests of significance? Choose the best answer.

  1. More than one of these answers is correct.
  2. The specification of a confidence level is the third step in the hypothesis testing process.
  3. Determining the significance level of a hypothesis test after calculating the test statistic can lead to an erosion of objectivity.
  4. The significance level is denoted by the Greek letter theta.
  5. The confidence level can be found by (1 - the probability of a Type I error).
  6. The significance level is equal to the probability of a Type I error.

Answer(s): D

Explanation:

The significance level is denoted by the Greek letter alpha. The significance level is equal to the probability of a Type I error, and can be found by subtracting the confidence level from the letter one. The relationship between the confidence level and the significance level is illustrated as follows:
Confidence level = (1 - significance level)
which can also be expressed as:
Confidence level = (1 - probability of a Type I error).
The Greek letter theta is used to represent the population parameter in the null and alternate hypotheses.
The remaining answers are all correct. It is important to remember that the level of significance should be determined prior to the calculation of the test statistic. Specifying the significance level after the calculation of the test statistic can detract from the objectivity of the test.






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