Inaudible in the caterer of a babies health is weight gain in the first year of the babies life. Assume that the population are such weekend for baby boys is approximately normally distributed. He said he claimed that the mean of this population is 4.93 KG. As a participating pediatrician you want to test is claim so you select a random sample of 16 baby boys and you record the weight each gained in the first year. Follow the steps below to construct a 99% confidence interval for the population mean of all the weekends for baby boys in the first year than state whether the confidence interval you construct contradicts the study’s claims. Sample standarddeviationNumber of baby boysSample meanTake Sample165.4961.873Enter 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 yalues provided.) When you are done, select "Compute".Sample size:Standard error:Point estimate:Critical valuesSample standard deviation:Margin of error:0.00s-2.947f0.010 =2.602Critical value:f0.025 -2.13199% confidence interval:0.050 -1.753Compute0.100-1.341(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:ExplanationChecko2021 McGraw-Hil Education. Al Rights Reserved Terms of Use I Privacy I AccessibilityMacBook Air*888 4FI%232$%&2358ERYPADGHKCVBaltoncommandcommandoptiomV (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:0.00010.0005.0000.0002.0004.0006.0008.00010.000(c)Does the 99% confidence interval you constructed contradict the claim made by the study?Choose the best answer from the choices below.O No, the confidence interval does not contradict the claim. The mean of 4.93 kg from the study is inside the 99%confidence interval.O No, the confidence interval does not contradict the claim. The mean of 4.93 kg from the study is outside the 99%confidence interval.O Yes, the confidence interval contradicts the claim. The mean of 4.93 kg from the study is inside the 99% confidenceinterval.O Yes, the confidence interval contradicts the claim. The mean of 4.93 kg from the study is outside the 99% confidenceinterval.ExplanationCheckO 2021 McGraw HI Education. AllRights Reserved Terms of UsePrivacyI AccessibiltyMacBook Air%23%&46.8QEYAGHKCValtaltotioncommandcommandoptic

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Inaudible in the caterer of a babies health is weight gain in the first year of the babies life. Assume that the population are such weekend for baby boys is approximately normally distributed. He said he claimed that the mean of this population is 4.93 KG. As a participating pediatrician you want to test is claim so you select a random sample of 16 baby boys and you record the weight each gained in the first year. Follow the steps below to construct a 99% confidence interval for the population mean of all the weekends for baby boys in the first year than state whether the confidence interval you construct contradicts the study’s claims.

Sample standard
deviation
Number of baby boys
Sample mean
Take Sample
16
5.496
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 yalues provided.) When you are done, select "Compute".
Sample size:
Standard error:
Point estimate:
Critical values
Sample standard deviation:
Margin of error:
0.00s-2.947
f0.010 =2.602
Critical value:
f0.025 -2.131
99% confidence interval:
0.050 -1.753
Compute
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:
Explanation
Check
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(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:
0.000
10.000
5.000
0.000
2.000
4.000
6.000
8.000
10.000
(c)
Does the 99% confidence interval you constructed contradict the claim made by the study?
Choose the best answer from the choices below.
O No, the confidence interval does not contradict the claim. The mean of 4.93 kg from the study is inside the 99%
confidence interval.
O No, the confidence interval does not contradict the claim. The mean of 4.93 kg from the study is outside the 99%
confidence interval.
O Yes, the confidence interval contradicts the claim. The mean of 4.93 kg from the study is inside the 99% confidence
interval.
O Yes, the confidence interval contradicts the claim. The mean of 4.93 kg from the study is outside the 99% confidence
interval.
Explanation
Check
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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Step 1

Confidence interval is an inference process which gives the range of plausible values of the population parameter. If the sample size is small, then the t distribution is used to find the confidence interval of population mean.

The standard error for sample mean is computed by $S E = \frac{s}{\sqrt{n}}$ , where s is sample standard deviation and n is the sample size. The margin of error is computed by multiplying the standard error to critical t value. The critical t value is the value corresponding to right tail area equal to $\frac{α}{2} = \frac{1}{2} (1 - \frac{C L}{100})$ , where CL is confidence level.

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