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Answer :
Final answer:
The 95% confidence interval for the average amount spent on books for all students is $162.93 to $177.07.
Explanation:
To find the 95% confidence interval for the average amount spent on books for all students, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √Sample Size)
Given information:
- Sample Mean (x) = $170
- Standard Deviation (σ) = $25.50
- Sample Size (n) = 50
- Critical Value (z) for 95% confidence level = 1.96
Plugging these values into the formula:
Confidence Interval = $170 ± (1.96) * ($25.50 / √50)
Calculating the values:
Confidence Interval = $170 ± (1.96) * ($25.50 / 7.07)
Confidence Interval = $170 ± (1.96) * $3.61
Confidence Interval = $170 ± $7.07
Therefore, the 95% confidence interval for the average amount spent on books for all students is $162.93 to $177.07.
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