Question

A building inspector believes that the percentage of new construction with serious code violations may be even greater than the previously claimed 7%. She conducts a hypothesis test on 200 new homes and finds 23 with serious code violations. Is this strong evidence against the .07 claim?

Answer 1

Yes, because the p-value is 0.0062

Explanation:

I looked it up on like 5 other websites and they all said this was the answer. I'm way too lazy to do it on my own.

Answer 2

The inspector's claim has strong statistical evidence.

Explanation:

To answer this we have to perform a hypothesis test.

The inspector claimed that the actual proportion of code violations is greater than 0.07, so the null and alternative hypothesis are:

`H_0: \pi\leq0.07\\\\H_a: \pi>0.07`

We assume a significance level of 0.05.

The sample size is 200 and the proportion of the sample is:

`p=(23)/(200)= 0.115`

The standard deviation is

`\sigma=\sqrt{(\pi(1-\pi))/(N) }= \sqrt{(0.07*0.93)/(200)}=0.018`

The z-value can be calculated as

`z=(p-\pi-0.5/N)/(\sigma) =(0.115-0.07-0.5/200)/(0.018) =(0.0425)/(0.018)=2.36`

The P-value for this z-value is P=0.00914.

This P-value is smaller than the significance level, so the effect is significant and the null hypothesis is rejected.

The inspector's claim has strong statistical evidence.