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Answer:
critical value = 1.645
The 90% confidence interval = ( -22.62, -17.58)
Step-by-step explanation:
Given that:
the sample size = 178
the sample size = 226
the sample mean = 54.4
the sample mean = 74.5
population standard deviation = 18.58
population standard deviation = 9.52
level of significance ∝ = 1 - 0.90 = 0.10
The critical value for is 1.645
For the construction of our confidence interval, we use 90% since that is used to find the critical value.
∴
The margin of error =
2.52
The lower limit =
= ( 54.4-74.5) - (2.52)
= -20.1 - 2.52
= -22.62
The upper limit =
= ( 54.4-74.5) + (2.52)
= -20.1 + 2.52
= -17.58
The 90% confidence interval = ( -22.62, -17.58)