Question

ERUISES PPLEMENTARY EXERCISES Applications 9 In the past a chemical plant has produced an average of 1,100 Ib of chemical per day. A random sample of 260 operating days from the past year shows that x = 1,040,im1gh Man The plant manager wishes to test whether the average daily production i has dropped significantly over the past year. . Do the data provide sufficient evidence to indicate a drop in average daily production?

Please show work on how you get the answer.

Answer 1

Given : n = 260
Given: n = 260 X^bar = 1040 s^2 = 130000 Therefore , s = 360.5551 mu_0 = 1100 alpha = 0.05 Hypothesis: H_0: mu = 1100 VS H_a: mu < 1100 The test statistic under Ho is , Z = X^bar - mu_0/s/squareroot n rightarrow N (0, 1) = 1040 - 1100/360.5551/squareroot 260 = -2.6833 Critical value: Z_alpha = Z_0.05 = 1.64 Decision Rule: Here , Z_stat = -2.6833 < -Z_alpha = -1.64 Therefore , reject Ho at 5% level of significance Conclusion: Hence , there is sufficient evidence to indicate a drop in average daily production.
$s^2=130000$ Therefore , s = 360.5551    $\mu_0=1100$    

Hypothesis : $H_0:\mu=1100$    Vs    $H_a:\mu<1100$

The test statistic under Ho is ,

$Z=\frac{\bar{X}-\mu_0}{s/\sqrt{n}}\to N(0,1)$

$=\frac{1040-1100}{360.5551/\sqrt{260}}=-2.6833$

Critical value : $Z_{\alpha}=Z_{0.05}=1.64$

Decision Rule : Here , $Z_{stat}=-2.6833<-Z_{\alpha}=-1.64$

Therefore , reject Ho at 5% level of significance

Conclusion : Hence , there is sufficient evidence to indicate a drop in average daily production.