Math  /  Data & Statistics

QuestionA Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53%53 \% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. The bootstrap distribution (based on 5,000 samples) is provided.
Would it be appropriate to use the normal distribution to construct the confidence interval in this situation? Yes No

Studdy Solution

STEP 1

1. The sample size is large enough for the Central Limit Theorem to apply.
2. The bootstrap distribution is approximately normal.
3. We are interested in constructing a confidence interval for the proportion of U.S. adults dissatisfied with the quality of education.

STEP 2

1. Evaluate the normality of the bootstrap distribution.
2. Determine the appropriateness of using the normal distribution for the confidence interval.

STEP 3

Examine the histogram of the bootstrap distribution. The distribution is centered around 0.529 and appears symmetric.

STEP 4

Check the standard deviation of the bootstrap distribution. The standard deviation is 0.016, which is relatively small compared to the range of the data.

STEP 5

Since the bootstrap distribution is approximately normal and the sample size is large (1,012), it is appropriate to use the normal distribution to construct the confidence interval.
The answer is:
Yes

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