1 If X is a normallydistributed random variable which of the

1:

If X is a normally-distributed random variable, which of the following conditions have to be true in order to use the z-distribution in single-sample confidence intervals and tests of hypothesis involving X? Choose all conditions that need to be true. Choose one answer.

The sample size has to be less than or equal to 30.

2:

If X and Y both have normal distributions, which of the following conditions have to be true in order to use the z-distribution in two-sample confidence intervals and tests of hypothesis involving X - Y? Choose all conditions that need to be true. Choose one answer.

Solution

1.

OPTION B: The variance is not estimated from the sample [ANSWER]

This is so because we have to use the actual population standard deviation itself for small samples.

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2.

OPTION A: The variances are not estimated from the samples.

This is by the same reason above: because we have to use the actual population standard deviation itself for small samples.