Answer:
We do not have sufficient evidence to reject the claim that ,the rate of inaccurate orders is equal to 10%.
Step-by-step explanation:
We want to use a 0.01 significance level to test the claim that the rate of inaccurate orders is equal to 10%.
We set up our hypothesis to get:
------->null hypothesis
------>alternate hypothesis
This means that: ![p_0=0.10](https://tex.z-dn.net/?f=p_0%3D0.10)
Also, we have that, one restaurant had 36 orders that were not accurate among 324 orders observed.
This implies that: ![\hat p=\frac{36}{324}=0.11](https://tex.z-dn.net/?f=%5Chat%20p%3D%5Cfrac%7B36%7D%7B324%7D%3D0.11)
The test statistics is given by:
![z=\frac{\hat p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B%5Chat%20p-p_0%7D%7B%5Csqrt%7B%5Cfrac%7Bp_0%281-p_0%29%7D%7Bn%7D%20%7D%20%7D)
We substitute to obtain:
![z=\frac{0.11-0.1}{\sqrt{\frac{0.1(1-0.1)}{324} } }](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B0.11-0.1%7D%7B%5Csqrt%7B%5Cfrac%7B0.1%281-0.1%29%7D%7B324%7D%20%7D%20%7D)
This simplifies to:
![z=0.6](https://tex.z-dn.net/?f=z%3D0.6)
We need to calculate our p-value.
P(z>0.6)=0.2743
Since this is a two tailed test, we multiply the probability by:
The p-value is 2(0.2723)=0.5486
Since the significance level is less than the p-value, we fail to reject the null hypothesis.
We do not have sufficient evidence to reject the claim that ,the rate of inaccurate orders is equal to 10%.