Question

follow the steps below to construct a 99% confidence interval for the population mean of all the weight gains for baby boys in their first year. then state whether the confidence interval you construct contradicts the studys claim. (if necessary, consult a .) (a) click on \take sample\ to see the results for your random sample. number of baby boys 16 sample mean 5.496 sample standard deviation 1.873 enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your 99% confidence interval. (choose the correct critical value from the table of critical values provided.) when you are done, select \compute\. sample size: point estimate: sample standard deviation: critical value: standard error: margin of error: 99% confidence interval: t_{0.005}=2.947 t_{0.010}=2.602 t_{0.025}=2.131 t_{0.050}=1.753 t_{0.100}=1.341 (b) based on your sample, graph the 99% confidence interval for the population mean of all the weight gains for baby boys 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 4.93 from the study. 99% confidence interval: (c) does the 99% confidence interval you constructed contradict the claim made by the study? choose the best answer from the choices below. - no, the confidence interval does not contradict the claim. the mean of 4.93 kg from the study is inside the 99% confidence interval. - no, the confidence interval does not contradict the claim. the mean of 4.93 kg from the study is outside the 99% confidence interval. - yes, the confidence interval contradicts the claim. the mean of 4.93 kg from the study is inside the 99% confidence interval. - yes, the confidence interval contradicts the claim. the mean of 4.93 kg from the study is outside the 99% confidence interval.

Explanation:

Step1: Identify sample values

Sample size \(n=16\), sample mean \(\bar{x}=5.496\), sample standard deviation \(s=1.873\)

Step2: Find critical t-value

Degrees of freedom \(df=n-1=15\), 99% confidence: \(t_{0.005,15}=2.947\)

Step3: Calculate standard error

Standard error \(SE=\frac{s}{\sqrt{n}}=\frac{1.873}{\sqrt{16}}=0.46825\)

Step4: Compute margin of error

Margin of error \(ME=t \times SE=2.947 \times 0.46825≈1.380\)

Step5: Calculate confidence interval

Lower limit: \(5.496 - 1.380≈4.116\); Upper limit: \(5.496 + 1.380≈6.876\)

Step6: Check study claim (4.93)

4.93 is inside [4.116, 6.876]

Answer:

(a) Sample size: 16; Point estimate: 5.496; Sample standard deviation: 1.873; Critical value: 2.947
(b) Lower limit≈4.116, Upper limit≈6.876
(c) No, the confidence interval does not contradict the claim. The mean of 4.93 kg from the study is inside the 99% confidence interval.