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FRM Part I · FRM Exam Part I · Hypothesis Testing

A researcher tests H0: mu = 5 against H1: mu > 5 using a sample of 64 observations with a known population standard deviation of 4. The sample mean is 5.9. What is the z-statistic and the approximate one-tailed p-value?

The standard error is 4/8 = 0.5, so z = 0.9/0.5 = 1.80. The upper-tail probability is about 0.036, which is the one-tailed p-value. Doubling it to 0.072 would apply only to a two-sided alternative.

  1. Az = 1.80; p-value about 0.036Correct
  2. Bz = 1.80; p-value about 0.072
  3. Cz = 0.23; p-value about 0.41
  4. Dz = 1.13; p-value about 0.13

Explanation

Standard error = 4/sqrt(64) = 0.5. z = (5.9 - 5)/0.5 = 1.80. One-tailed p = 1 - N(1.80) = 1 - 0.9641 = 0.0359. The 0.072 option wrongly doubles the p-value for a one-sided alternative.

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