Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
The 99% confidence interval for the difference between the mean fill volumes at the two locations is;
-0.1175665 L < μ₁ - μ₂ < 0.1295665 L
Step-by-step explanation:
The number of bottles in the sample at the first location, n₁ = 18 bottles
The mean fill volume, [tex]\bar{x}_{1}[/tex] = 2.007 L
The standard deviation, σ₁ = 0.010 L
The number of bottles in the sample at the second location, n₂ = 10 bottles
The mean fill volume, [tex]\bar{x}_{2}[/tex] = 2.001 L
The standard deviation, σ₂ = 0.012 L
The nature of the variance of the two samples = Equal variance
The confidence interval of the statistics, C = 99%
The difference between the mean
[tex]\mu_1 - \mu_2 = \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2} \times \sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}+\dfrac{\sigma _{2}^{2}}{n_{2}}}[/tex]
(1 - C)/2 = (1 - 0.99)/2 = 0.005, the degrees of freedom, f = n₁ - 1 = 10 - 1 = 9
∴ [tex]t_{\alpha /2}[/tex] = 3.25
Therefore, we have;
[tex]\mu_1 - \mu_2 = \left (2.007- 2.001 \right )\pm 3.25 \times \sqrt{\dfrac{0.01^{2}}{18}+\dfrac{0.12^{2}}{10}}[/tex]
Therefore, we have the difference of the two means given as follows;
-0.1175665 L < μ₁ - μ₂ < 0.1295665 L
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
