Here are summary statistics for randomly selected weights of newborn girls: nequals177, x overbarequals28.9 hg, sequals6.7 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 28.1 hgless thanmuless than30.7 hg with only 20 sample values, x overbarequals29.4 hg, and sequals2.3 hg? What is the confidence interval for the population mean mu?

Question:

Here are summary statistics for randomly selected weights of newborn girls: n = 177, x = 28.9 hg, s = 6.7 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 28.1 hg < μ < 30.7 hg with only 20 sample values, x' =29.4 hg, and s = 2.3 hg? What is the confidence interval for the population mean μ?

The confidence interval for the population mean μ is 27.73  ≤ μ ≤ 30.0714

Step-by-step explanation:

The equation to identify the confidence interval for the mean is given by

Where

x' = Sample mean = 28.9

s = Standard deviation = 6.7

n = Sample size = 177

= Critical value =  2.326

Therefore we have

27.73  ≤ μ ≤ 30.0714

  T test we have

t =  

= = 0.8696      which is < 1      

df = 15 as sample size = 15

Upper tail statistics lies between 0.3 and 0.1