Question

Can some one help me on this question?
It is thought that more than 10% of all new cars sold have defects that will cause them to be returned to the shop for major repairs within 1 year.
a. Set up the null appropriate null and alternate hypotheses to verify this contention.
b. A particular dealer samples 15 records from her files. It is found that three were returned for major repairs during the first year of operation. Find the P value for the test. Do you think that H0 should be rejected based on these data? Explain.

Answer 1

a)
Ho: p=0.1 (or p<=0.1)
Ha:p>0.1 (claim)
b)Assuming Ho (p=0.1) is true, we need to calculate the probability that in a sample of 15 we get 3 or more cars returned for repair. In our case, the formula would be:
\[P(k \ge 3)=1-P(k \le 2)=1-\sum_{k=0}^{2}\left(\begin{matrix}15 \\ k\end{matrix}\right)0.1^k·0.9^{15-k}=1-0.816=0.184\]
This probability of P= 18.4%>5% indicates that we fail to reject the null hypothesis

Answer 2

Thank you very much

Answer 3

welcome