Answer to Question #125506 in Statistics and Probability for jse

Question

Let the sample size of the television tube brightness experiment be ten and the sample mean and sample standard deviation be 315.4 microamps and 13.6 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.

H0: mu =

_________, H1: mu ( >, <, not equal) _________

Find the P-value for this test.

A. 0.25 < P-value < 0.50
B. 0.0005 < P-value < 0.0010
C. 0.0025 < P-value < 0.0050
D. 0.025 < P-value < 0.050

With a significance level of a = 0.05 ( fail to reject, reject ) H0.

For this test, we assumed that the underlying distribution of the data is a t-distribution.
A. True
B. False

Answer 1

Solution:

The provided sample mean is $\bar X = 315.4$  and the sample standard deviation is s = 13.6, and the sample size is n = 10

(1) Null and Alternative Hypotheses

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:

$t=\frac{\overline{x}-\mu _{0}}{\frac{s}{\sqrt{n}}}$

$\frac{315.4-300}{\frac{13.6}{\sqrt{10}}}$ =3.581

Using the P-value approach:Using degrees of freedom = n-1= 10-1=9, and alpha = 0.05 using ti84 or software, the p-value is p = 0.003

and since p=0.003<0.05, it is concluded that the null hypothesis is rejected.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 300, at the 0.05 significance level.