Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Using the t-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that Battery B outlasts Battery A by more than 2 hours.
At the null hypothesis, it is tested if it does not outlast by more than 2 hours, that is, the subtraction is not more than 2:
[tex]H_0: \mu_B - mu_A \leq 2[/tex]
At the alternative hypothesis, it is tested if it outlasts by more than 2 hours, that is:
[tex]H_1: \mu_B - \mu_A > 2[/tex]
- The sample means are: [tex]\mu_A = 8.65, \mu_B = 11.23[/tex]
- The standard deviations for the samples are [tex]s_A = s_B = 0.67[/tex]
Hence, the standard errors are:
[tex]s_{Ea} = S_{Eb} = \frac{0.67}{\sqrt{12}} = 0.1934[/tex]
The distribution of the difference has mean and standard deviation given by:
[tex]\overline{x} = \mu_B - \mu_A = 11.23 - 8.65 = 2.58[/tex]
[tex]s = \sqrt{s_{Ea}^2 + s_{Eb}^2} = \sqrt{0.1934^2 + 0.1934^2} = 0.2735[/tex]
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 2[/tex] is the value tested at the hypothesis.
Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{2.58 - 2}{0.2735}[/tex]
[tex]t = 2.12[/tex]
The critical value for a right-tailed test, as we are testing if the subtraction is greater than a value, with a 0.05 significance level and 12 + 12 - 2 = 22 df is given by [tex]t^{\ast} = 1.71[/tex]
Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that Battery B outlasts Battery A by more than 2 hours.
A similar problem is given at https://brainly.com/question/13873630
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
