Answer to Question #127579 in Statistics and Probability for jessica

Question

Let the sample size of the television tube brightness experiment be ten and the sample mean and sample standard deviation be 317.2 microamps and 15.7 microamps, respectively. Suppose that the design engineer claims that this tube will require at least 300 microamps of current to produce the desired brightness level.

Choose an appropriate hypothesis to test.

Find the P-value for this test.

0.25 < P-value < 0.50
0.025 < P-value < 0.050
0.0025 < P-value < 0.0050
0.0005 < P-value < 0.0010

Answer 1

The provided sample mean is $\bar X = 317.2$

and the sample standard deviation is s = 15.7, and the sample size is n = 10.

The following null and alternative hypotheses need to be tested:

Ho: μ = 300

Ha: μ > 300

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

The t-statistic is computed as follows:

$t=\frac{\overline{X}-mean}{\frac{s}{\sqrt{n}}}$

=$t=\frac{317.2-300}{\frac{15.7}{\sqrt{10}}}$ =3.464

Using the P-value approach:Degrees of freedom = n- 1= 10-1=9 and alpha= 0.05 , using t i84 we get the p-value is p = 0.0036.

Hence 0.0025 < P-value < 0.0050

Since p=0.0036<0.05, it is concluded that the null hypothesis is rejected.