Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Question:
The mean lifetime of 100 mobile phones in a sample is 1,500 hours and their standard deviation is 120 hours, u is the mean lifetime of all the mobile phones produced. Perform a test of hypothesis that the sample comes from a population whose mean is 1,600 hours at 586 significance level 10 marks​

Sagot :

Using the t-distribution, as we have the standard deviation for the sample, it is found that since the absolute value of the test statistic is greater than the critical value for the two-tailed test, there is enough evidence to conclude that the sample does not come from a population whose mean is 1,600 hours.

What are the hypothesis tested?


At the null hypothesis, it is tested if the mean is of 1600 hours, that is:

[tex]H_0: \mu = 1600[/tex]

At the alternative hypothesis, it is tested if the mean is different of 1600 hours, that is:

[tex]H_1: \mu \neq 1600[/tex]

What is the test statistic?

It is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

  • [tex]\overline{x}[/tex] is the sample mean.
  • [tex]\mu[/tex] is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

In this problem, the values of the parameters are:

[tex]\overline{x} = 1500, \mu = 1600, s = 120, n = 100[/tex]

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{1500 - 1600}{\frac{120}{\sqrt{100}}}[/tex]

[tex]t = -8.33[/tex]

What is the decision rule?


Considering a two-tailed test, as we are testing if the mean is different of a value, with 100 - 1 = 99 df and a significance level of 0.01, the critical value is of [tex]t^{\ast} = 1.66[/tex].

Since the absolute value of the test statistic is greater than the critical value for the two-tailed test, there is enough evidence to conclude that the sample does not come from a population whose mean is 1,600 hours.

More can be learned about the t-distribution at https://brainly.com/question/13873630

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.