2. The data below shows the birth weights (in kilograms) of thirty randomly chos

Question

2. The data below shows the birth weights (in kilograms) of thirty randomly chosen male babies born in Hays Medical in past year. It is also known that the population standard deviation of birth weights for all male babies born is 0.0731 kg (based on data from the New York State Department of Health). 3.73 4.37 3.73 4.33 3.3 3.39 3.68 4.68 3.72 3.02 3.96 2.21 2.67 4.09 3.02 2.76 3.67 3.76 3.45 2.54 2.55 3.44 3.07 4.23 2.92 3.55 3.92 3.41 4.14 3.15 a. How do you know that you will need to construct the confidence interval using a z-distribution approach as opposed to a t-distribution? We want to construct the mean value confidence interval for all Hays male babies' birth weights with a 99% confidence level. b. Determine the best point estimate (average) for the mean birth weight. c. Determine the critical z-value(s) associated with the 99% confidence level. d. Determine the margin of error. e. Determine the confidence interval. f. In a sentence, interpret the contextual meaning of your result to part e above...that is relate the values to this situation regarding the mean birth weights of all Hays male babies born. 2. The data below shows the birth weights (in kilograms) of thirty randomly chosen male babies born in Hays Medical in past year. It is also known that the population standard deviation of birth weights for all male babies born is 0.0731 kg (based on data from the New York State Department of Health). 3.73 4.37 3.73 4.33 3.3 3.39 3.68 4.68 3.72 3.02 3.96 2.21 2.67 4.09 3.02 2.76 3.67 3.76 3.45 2.54 2.55 3.44 3.07 4.23 2.92 3.55 3.92 3.41 4.14 3.15 a. How do you know that you will need to construct the confidence interval using a z-distribution approach as opposed to a t-distribution? We want to construct the mean value confidence interval for all Hays male babies' birth weights with a 99% confidence level. b. Determine the best point estimate (average) for the mean birth weight. c. Determine the critical z-value(s) associated with the 99% confidence level. d. Determine the margin of error. e. Determine the confidence interval. f. In a sentence, interpret the contextual meaning of your result to part e above...that is relate the values to this situation regarding the mean birth weights of all Hays male babies born.

Explanation / Answer

Part-a

As sample size is large (n=30) and population standard deviation is known, so we will need to construct the confidence interval using a z-distribution approach as opposed to a t-distribution?

Part-b

Sample mean=3.482

Part-c

Critical Z=± 2.58

Part-d

Margin of error ME= Z0.01/2*/sqrt(n)

=2.58*0.0731/sqrt(30)

=0.034

Part-e

99% confidence interval=xbar-ME, xbar+ME

=3.482-0.034 , 3.482+0.034

=(3.448                 3.516)

Part-f

We are 99% confident that the true mean birth weights of all Hays male babies born is contained by this interval.

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