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 μ and its 90% margin of error.
b. A 95% confidence interval for μ.

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 .

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  

=>    

=>    

y=mx+

step-by-step explanation: