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Complete Question
From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval obtain:
a. A point estimate of and its 90% margin of error.
b. A 95% confidence interval for .
Answer:
a
.
b
Step-by-step explanation:
From the question we are told that
The sample size is n = 18
The 90% confidence interval is (11.1, 15.7)
Generally the point estimate of is mathematically evaluated as
=>
Generally the margin of error is mathematically evaluated as
=>
From the question we are told the confidence level is 90% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the equation for the lower limit of the confidence interval is
=>
=>
From the question we are told the confidence level is 95% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the margin of error is mathematically represented as
=>
=>
Generally 95% confidence interval is mathematically represented as
=>
=>