Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
The null hypothesis is [tex]H_0: \mu = 26.5[/tex]
The alternate hypothesis is [tex]H_a: \mu > 26.5[/tex]
The pvalue of the test is 0.1075 > 0.05, which means that there is not sufficient evidence at the 0.05 level to support the testing firm's claim.
Step-by-step explanation:
An automobile manufacturer has given its jeep a 26.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep performs over the manufacturer's MPG rating.
At the null hypothesis, we test that the mean is 26.5 MPG, that is:
[tex]H_0: \mu = 26.5[/tex]
At the alternate hypothesis, we test that the mean is above 26.5 MPG, that is:
[tex]H_a: \mu > 26.5[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
26.5 is tested at the null hypothesis:
This means that [tex]\mu = 26.5[/tex]
After testing 240 jeeps, they found a mean MPG of 26.7. Assume the population standard deviation is known to be 2.5.
This means that [tex]n = 240, \mu = 26.7, \sigma = 2.5[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{26.7 - 26.5}{\frac{2.5}{\sqrt{240}}}[/tex]
[tex]z = 1.24[/tex]
Pvalue of the test and decision:
The pvalue of the test is the probability of finding a mean above 26.7, which is 1 subtracted by the pvalue of z = 1.24.
Looking at the z-table, z = 1.24 has a pvalue of 0.8925
1 - 0.8925 = 0.1075
The pvalue of the test is 0.1075 > 0.05, which means that there is not sufficient evidence at the 0.05 level to support the testing firm's claim.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
