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Answer :
Final answer:
The 95% confidence interval for the average spent on books for all students is approximately $162.93 to $177.07.
Explanation:
To calculate a 95% confidence interval for the average spent on books for all students, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
First, we need to calculate the standard error, which is the standard deviation of the sample divided by the square root of the sample size:
Standard Error = Standard Deviation / √(Sample Size)
Given that the sample mean is $170, the standard deviation is $25.50, and the sample size is 50, we can calculate the standard error:
Standard Error = $25.50 / √(50) ≈ $3.61
Next, we need to find the critical value for a 95% confidence level. Since the population is assumed to be normal, we can use the Z-table to find the critical value. For a 95% confidence level, the critical value is approximately 1.96.
Now, we can calculate the confidence interval:
Confidence Interval = $170 ± (1.96 * $3.61)
Simplifying the expression:
Confidence Interval ≈ $170 ± $7.07
Therefore, the 95% confidence interval for the average spent on books for all students is approximately $162.93 to $177.07.
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