Thank you for visiting The scores on the Wechsler Intelligence Scale for Children WISC are known to be normally distributed with a standard deviation of 10 A simple random. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The 99% confidence interval for the mean of the scores on the WISC is approximately 95.96 to 103.64.
To find a 99% confidence interval for the mean of the scores on the Wechsler Intelligence Scale for Children (WISC), we can use the formula:
Confidence interval = sample mean ± (critical value) * (standard deviation / √sample size)
First, we need to find the critical value associated with a 99% confidence level. Since the sample size is large (n > 30), we can use the Z-table to find the critical value. For a 99% confidence level, the critical value is approximately 2.576.
Next, we plug in the values into the formula:
Confidence interval = 99.8 ± (2.576) * (10 / √45)
Calculating the values:
Confidence interval = 99.8 ± (2.576) * (10 / √45)
Confidence interval = 99.8 ± (2.576) * (10 / 6.708)
Confidence interval = 99.8 ± (2.576) * 1.491
Now, we can calculate the lower and upper bounds of the confidence interval:
Lower bound = 99.8 - (2.576) * 1.491
Upper bound = 99.8 + (2.576) * 1.491
Calculating the values:
Lower bound ≈ 99.8 - 3.84
Lower bound ≈ 95.96
Upper bound ≈ 99.8 + 3.84
Upper bound ≈ 103.64
Therefore, the 99% confidence interval for the mean of the scores on the WISC is approximately 95.96 to 103.64.
In the context of this scenario, we can say with 99% confidence that the true mean score on the WISC for the population of children lies between 95.96 and 103.64.
Learn more about critical value from the below link
https://brainly.com/question/32591251
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