Question

can someone help with this and expand on the concepts / answers

3. If you obtained one thousand 90% confidence intervals for a population mean, µ, roughly how many would actually contain µ?

4. The height of ten year old girls has a mean 4.5 and standard deviation 1.5
   1. If you want to make a confidence interval for the population mean of the heights, what assumption must you make about the population distribution of heights?
   2. Make the assumption you choose and let xbar = 3.9 from a sample of 36 ten year old girls, calculate a 90% confidence interval (CI) for µ.

Answer 1

If you obtained one thousand 90% confidence intervals for a population mean, µ, roughly how many would actually contain µ.

Ans : 1000 (all the confidence intervals should contain population mean)

If you want to make a confidence interval for the population mean of the heights, what assumption must you make about the population distribution of heights?

Ans: Population must be Normally distributed.

Sample mean=r= 3.9 Population S.D=0= 1.5 Sample size=n= 36 Significance Level = a = 0.1 Critical value ==* = 1.645 Standard Error = * = 0.2500 Margin of Error ==* = 0.4112 Lower Limit = 8 – (Margin of Error) = 3.4888 Upper Limit=x+(Margin of Error) = 4.3112 The 90% C.I is ( 3.4888, 4.3112 ) or 3.4888 < p < 4.3112.