A notable indicator of a baby's health is the weight gained in the first year of the baby's life. Assume that the population of all such weight gains for baby girlsis approximately normally distributed. A study claimed that the mean of this population is 5.94 kg. As a practicing pediatrician, you want to test this claim. So,you select a random sample of 15 baby girls, and you record the weight each gained in their first year.Follow the steps below to construct a 95% confidence interval for the population mean of all the weight gains for baby girls in their first year. Then statewhether the confidence interval you construct contradicts the study's claim. (If necessary, consult a list of formulas.)(a) Click on "Take Sample" to see the results for your random sample.Take SampleSample size:0Point estimate:0Sample standard deviation:10Critical value:0Number of baby girlsCompute15Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your 95%confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".Sample mean5.658Standard error:Margin of error:Sample standarddeviation95% confidence interval:1.869XCritical values¹0.005 2.977¹0.010 2.62410.025 2.14510.050 1.761¹0.100=1.345 (b) Based on your sample, graph the 95% confidence interval for the population mean of all the weight gains for baby girls in their first year.• Enter the values for the lower and upper limits on the graph to show your confidence interval.• For the point (), enter the claim 5.94 from the study.(c)0.0000.0002,00095% confidence interval:4.0005.0006.0008.000Does the 95% confidence interval you constructed contradict the claim made by the study?Choose the best answer from the choices below.10.00010.000ŚO No, the confidence interval does not contradict the claim. The mean of 5.94 kg from the study is inside the 95%confidence interval.O No, the confidence interval does not contradict the claim. The mean of 5.94 kg from the study is outside the 95%confidence interval.Yes, the confidence interval contradicts the claim. The mean of 5.94 kg from the study is inside the 95% confidenceinterval.Yes, the confidence interval contradicts the claim. The mean of 5.94 kg from the study is outside the 95%confidence interval.X3

From given data we have ; sample size =15 Point estimate = 5.658 standard deviation =1.869 here the population standard deviation, is unknown and hence we need to use t statistic for our analysis sample size =15 Point estimate = 5.658 standard deviation =1.869 critical value is given by tα2,n-1=t0.052,15-1 =t0.025,14 =2.145 Standard Error (SE) is given by SE=sn =1.86915 =0.4826 the Margin of Error ME=t0.025×SE =2.145×0.4826 =1.035295 % confidence interval x¯±ME5.658±1.0352(4.6228,6.6932)yes , the confidence interval does contradict the claim. The mean of 5.94 kg from the study is inside the 95% confidence interval.No, the confidence