Question

The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. A random sample of 15 devices is selected and found to have an average life of 5323.8 hours and a sample standard deviation of 220.9 hours.
Test the hypothesis that the true mean life of a biomedical device is greater than 5200.

Answer 1

Answer:

We conclude that the true mean life of a biomedical device is greater than 5200 hours.

Step-by-step explanation:

We are given that the life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. For this a random sample of 15 devices is selected and found to have an average life of 5323.8 hours and a sample standard deviation of 220.9 hours.

We have to test that the true mean life of a biomedical device is greater than 5200 or not.

Let, Null Hypothesis, $H_0$ : $\mu \leq$ 5200 {means that the true mean life of a biomedical device is less than or equal to 5200 hours}

Alternate Hypothesis, $H_1$ : $\mu$ > 5200 {means that the true mean life of a biomedical device is greater than 5200 hours}

The test statistics that will be used here is;

        T.S. = $\frac{Xbar-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, Xbar = sample average life = 5323.8 hours

               s = sample standard deviation = 220.9 hours

               n = sample devices = 15

So, test statistics = $\frac{5323.8-5200}{\frac{220.9}{\sqrt{15} } }$ ~ $t_1_4$

                            = 2.171

Since, we are not given with the significance level, so we assume it to be 5%, now the critical value of t at 14 degree of freedom in t table is given as 1.761. Since our test statistics is more than the critical value of t which means our test statistics will lie in the rejection region. So, we have sufficient evidence to reject our null hypothesis.

Therefore, we conclude that the true mean life of a biomedical device is greater than 5200 hours.