Which of the below Z scores is the appropriate z* when calculating a 98% confidence interval? (a) Z = 2.05 (b) Z = 1.96 (c) Z = 2.33 (d) Z = -2.33 (e) Z = -1.65

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**Question**: Which of the below Z scores is the appropriate \( z^* \) when calculating a 98% confidence interval?

**Options**:
(a) \( Z = 2.05 \)

(b) \( Z = 1.96 \)

(c) \( Z = 2.33 \)

(d) \( Z = -2.33 \)

(e) \( Z = -1.65 \)

When calculating a 98% confidence interval, the correct \( z^* \) value represents the Z score that encompasses the central 98% of the standard normal distribution, leaving 1% in each tail. Therefore, the correct answer is:

(c) \( Z = 2.33 \)

This Z score corresponds to the positive critical value needed for a 98% confidence interval. A negative value (like in options d and e) is incorrect in this context because confidence intervals conventionally use the positive Z score.
Transcribed Image Text:**Question**: Which of the below Z scores is the appropriate \( z^* \) when calculating a 98% confidence interval? **Options**: (a) \( Z = 2.05 \) (b) \( Z = 1.96 \) (c) \( Z = 2.33 \) (d) \( Z = -2.33 \) (e) \( Z = -1.65 \) When calculating a 98% confidence interval, the correct \( z^* \) value represents the Z score that encompasses the central 98% of the standard normal distribution, leaving 1% in each tail. Therefore, the correct answer is: (c) \( Z = 2.33 \) This Z score corresponds to the positive critical value needed for a 98% confidence interval. A negative value (like in options d and e) is incorrect in this context because confidence intervals conventionally use the positive Z score.
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