问题


There is a single choice question about high school statistics. Answer the question by replying A, B, C or D.
Question: You need to construct a 94% confidence interval for a population proportion. What is the upper critical value of z to be used in constructing this interval?
A. 0.9699
B. 1.96
C. 1.555
D. 1.88
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

D. 1.88
D
deepseekr1

To construct a 94% confidence interval for a population proportion, the upper critical z-value is determined by the cumulative probability corresponding to the middle 94% of the standard normal distribution. This leaves 6% in the tails, with 3% (0.03) in each tail. The critical value \( z^* \) is the point where the cumulative probability to the left is \( 1 - 0.03 = 0.97 \).

Using the standard normal distribution table or calculator:
- A z-score of **1.88** corresponds to a cumulative probability of approximately **0.9699** (close to 0.97).
- Common critical values like 1.96 (for 95% confidence) or 1.555 are not applicable here.

Thus, the correct upper critical value is **1.88**, corresponding to **Option D**.

**Answer: D**
D
gpto1 D D
GPT-4o D. 1.88 D
llama3.1-70B-Instruct

B
D
llama3.1-405B-Instruct

D
D
DeepSeek-Coder-V2 D. 1.88 D
Qwen2-72B-Instruct To find the upper critical value of z for a 94% confidence interval, we need to find the z-score that corresponds to the upper 3% in the standard normal distribution (since 94% leaves 6% in the tails, and half of that, 3%, is in the upper tail). Using a z-table or a calculator, we find that the z-score for the upper 3% is approximately 1.88.

Answer: D. 1.88
D
baichuan4 D. 1.88 D
doubao D. 1.88

For a 94% confidence interval, the significance level is 1 - 0.94 = 0.06. The critical value is the z-score that leaves 0.03 in the upper tail. Looking up in a standard normal table or using a calculator, the z-score corresponding to 0.03 in the upper tail is approximately 1.88.
D
minimax B. 1.96

The upper critical value of z for a 94% confidence interval is 1.96, because the confidence level corresponds to the area under the standard normal distribution curve that is centered around the mean. A 94% confidence interval means that 94% of the data lies within 1.96 standard deviations of the mean in both directions (97% on each side, leaving 3% in the tails of the distribution).
D
kimi D. 1.88 D
wenxinyiyan D D
zhipu To construct a 94% confidence interval for a population proportion, you need to find the critical value of z that corresponds to the middle 94% of the standard normal distribution. This means that 3% of the distribution is in each tail (since 100% - 94% = 6%, and 6% / 2 = 3%).

You need to find the z-score that leaves 3% in the upper tail. This is the same as finding the z-score for the 97th percentile (since 100% - 3% = 97%).

Looking up the z-score for the 97th percentile in a standard normal distribution table, you find:

The z-score corresponding to the 97th percentile is approximately 1.88.

Therefore, the correct answer is:
D. 1.88
D
gpto1 D D
deepseekv3 To construct a 94% confidence interval for a population proportion, we need to find the upper critical value of z (z*) that corresponds to the middle 94% of the standard normal distribution. This means 3% of the area lies in each tail of the distribution.

Using a standard normal table or a calculator, we find that the z-score that leaves 3% in the upper tail is approximately **1.88**.

Thus, the correct answer is:

**D. 1.88**
D