Here are summary stastistics for randomly selected weights of newborn girls: n=224,overline{x}=28.3 text{hg},s=7.1 text{hg}. Construct a confidence interval estima

Khaleesi Herbert 2020-11-07 Answered

Here are summary stastistics for randomly selected weights of newborn girls: n=224,x=28.3hg,s=7.1hg. Construct a confidence interval estimate of mean. Use a 98% confidence level. Are these results very different from the confidence interval 26.5hg<μ<30.7hg with only 14 sample values, x=28.6 hg, and s=2.9 hg? What is the confidence interval for the population mean μ?

 27,2 hg<μ<29,4 hg? (Round to one decimal place as needed).

Are the results between the two confidence intervals very different?

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Expert Answer

Bentley Leach
Answered 2020-11-08 Author has 109 answers

Step 1 From the provided information, Sample size (n)=244 Sample mean (x)=28.3 hg Sample standard deviation (s)=7.1 hg Step 2 Since, the population standard deviation is unknown, therefore, the t distribution will be used. Confidence level = 98% Level of significance (α)=10.98=0.02 The degree of freedom =n1=2441=243 The critical value of t at 243 degree of freedom with 0.01 level of significance from the t value table is 2.34. Step 3 The required 98% confidence interval can be obtained as: CI=x±tα2,n1sn
=28.3±(2.34)7.1224
=28.3±1.1
=(27.2,29.4) Thus, the confidence interval is 27.2<μ<29.4. No, the results between the two confidence intervals are not very different. The confidence interval limits are almost similar.

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