Answer to Question #283862 in Statistics and Probability for Yabiy

Question

Copy Machine Use A store manager hypothesizes that the average number of pages a person copies on the store’s copy machine is less than 40. A sample of 50 customers’ orders is selected. At a _ 0.01, is there enough evidence to support the claim? Assume population standard deviation 30.9.

Answer 1

$n=50$

$s=30.9$

$\mu_0=40$

X = Number of pages a person copies on the store's copy machine

$\bar{X}=\frac{\Sigma X}{n}=\frac{1463}{50}=29.26$

Null & Alternative Hypothesis:

$H_0:\mu=\mu_0$

$H_a:\mu<\mu_0$

Test Statistic:

Sample size is greater than 30, so Z-test is appropriate to test null hypothesis.

$Z=\frac{\bar{X}-\mu}{\frac{\bar{s}}{\sqrt{n}}}$

$Z=\frac{29.26-40}{\frac{\bar{30.9}}{\sqrt{50}}}=-2.46$

Critical Value:

The level of significance is 0.01.

$Z_\alpha=Z_0.01=-2.326$

Statistical Decision:

Since, Z-test statistic is less than critical value (-2.46 < -2.326). So, the null hypothesis is rejected.

Conclusion:

It can conclude that average number of pages a person copies on the store's copy machine is less than 40.