Answer :
Final answer:
The question is asking to estimate the 90% confidence interval for the mean IQ of a population. Using the provided data (mean=101.2, standard deviation=17, and sample size=374), we can calculate the standard error and use a z-value for a 90% confidence level to find the confidence interval lies between 99.75 and 102.65.
Explanation:
The student wants to estimate the 90% confidence interval for the mean IQ of a population. This is a question of statistics, particularly dealing with confidence intervals and population means.
As the sample size is greater than 30, we can use the z-distribution for this estimation. In this case, the sample mean (Xbar) is 101.2, the standard deviation (s) is 17, and the sample size (N) is 374.
The standard error (SE) would be [tex]s/√N = 17/√374[/tex] = 0.88. For 90% confidence level, the z value from the z-table is 1.645.
So, the confidence interval is calculated as Xbar ± Z*SE. Substituting the values we get [tex]101.2 ± 1.645*0.88 = 101.2 ± 1.45[/tex]. Thus, we estimate that the 90% confidence interval for the mean IQ is between 99.75 and 102.65.
Learn more about Confidence Intervals
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