interested in the mean IQ score of a given group of children. It is known that the IQ scores of the group have a standard deviation of . The psychologist randomly selects children from this group and finds that their mean IQ score is . Based on this sample, find a confidence interval for the true mean IQ score for all children of this group. Then complete the table below.
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To find a confidence interval for the true mean IQ score of all children in the group, we'll use the following steps:
Step 1: Define the level of confidence.
The level of confidence represents the percentage of confidence we have in the interval estimate. Let's assume a level of 95% confidence, which is commonly used.
Step 2: Determine the sample size.
The sample size is denoted by "n". In your question, it is not specified, so we need that information to proceed further.
Step 3: Calculate the standard error.
The standard error measures the variability or dispersion of the sample mean. It is calculated by dividing the standard deviation of the population by the square root of the sample size (n). In this case, we are given the standard deviation of the group, but we still need the sample size to calculate the standard error.
Step 4: Determine the critical value.
The critical value is derived from the level of confidence and the sample size. It represents the number of standard errors away from the mean needed to achieve the desired level of confidence. The critical value can be obtained from a standard normal distribution table. Since the sample size is not mentioned, we will not be able to determine the exact critical value.
Once we have the sample size and the critical value, we can calculate the confidence interval using the formula:
Confidence Interval = Sample Mean ± (Critical Value × Standard Error)
Without the sample size and critical value, it's difficult to complete the table you mentioned. Please provide the sample size information, or any other details mentioned in the question, so we can proceed with the calculation and complete the table.