Question

A photo processing company sets a quality standard of no more than 10 complaints per week on average. A random sample of 8 weeks showed an average of 13.6 complaints, with standard deviation 5.3. Is the firm achieving its quality objective? Assume 10% level of significance and use p-value approach.

Answer 1

Let the mean number of complaints per week be denoted as $\mu$.

Null Hypothesis H₀: $\mu$=10 vs Alternate Hypothesis H₁: $\mu$<0

Given :-   sample size (n) = 8 ; sample mean ($\bar{x}$) = 13.6 ; sample standard deviation (s) = 5.3

We know ; $T=\frac{\sqrt{n}(\bar{x}-\mu)}{s}\sim t_{n-1}$ i.e T ~ t₇  

Under H₀ , t = observed value of T = $\sqrt{8}$$\times$(13.6 - 10)/5.3 = 1.9212

$p-value=P_{H_{0}}(T\leqslant t)=P(\frac{\sqrt{n}(\bar{x}-\mu)}{s}\leqslant 1.9212)=0.9519$

Given :- level of significance ($\alpha$) = 10% = 0.1

H₀ is rejected if p-value $\leqslant$$\alpha$

p-value = 0.9519 > 0.1 = $\alpha$

$\therefore$ H₀ is accepted

Thus it is concluded that mean number of complaints is more than 10.

The firm is not achieving its quality objective.

Answer 2

10 complaints