Question

The manufacturer of television tubes knows from the past experience that the average life of tube is 2000hrs with a s.d. of 200hrs . a sample of 100 tubes has an average life of 1950hrs. Test at the 0.01 level of significance to see if this sample came from a normal population of mean 2000hrs.

Answer 1

Answer:

100hrs

Step-by-step explanation:

I guess it's helpful to you

Answer 2

Given:

$\begin{array}{l}n=100 \\\bar{x}=1950 \\\sigma=200 \text { and } \alpha=0.01\end{array}$

we determine whether the population mean (μ) is equal to 2000hrs as claimed.

$H_{0}: \mu=2000$

Against

$H_{1}: \mu \neq 2000$

The test statistic is given as,

$\begin{array}{l}Z^{*}=(\bar{x}-\mu) /(\sigma / \sqrt{n}) \\Z^{*}=(1950-2000) /(200 / \sqrt{100})=-50 / 20=-2.5\end{array}$

$\text { The test statistic } Z^{*} \text { is compare with the table value at } \alpha=0.01 \text { significance level }$

$Z_{\alpha / 2}=Z_{0.01 / 2}=Z_{0.005}=2.575 \text { and the null hypothesis is rejected if }\left|Z^{*}\right|>Z_{0.005}$

$\text { Since }\left|Z^{*}\right|=|-2.5|=2.5<Z_{0.005}=2.575$

Hence sample came from a normal population of mean 2000 hours at 1% level of significance.