Question

b. compute the test statistic and associated p - value. (round each value as instructed.)
z = 1.99 (round your answer to two decimal places.)
p - value = 0.0466 (round your answer to four decimal places.)
c. what is the correct conclusion?
a. we should not reject ( h_0 ). there is sufficient evidence to conclude that the failure rate is different.
b. we should reject ( h_0 ). there is sufficient evidence to conclude that the failure rate is different.
c. we should reject ( h_0 ). there is insufficient evidence to conclude that the failure rate is different.
d. we should not reject ( h_0 ). there is insufficient evidence to conclude that the failure rate is different.
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Explanation:

Step1: Hypothesis testing rule

In hypothesis testing, if the P - value is less than the significance level ($\alpha$), we reject the null hypothesis ($H_0$). Here, assume the significance level $\alpha = 0.05$ (a common choice when not specified otherwise).

Step2: Compare P - value and $\alpha$

We are given that $P - value=0.0466$. Since $0.0466<0.05$ (our assumed $\alpha$), we reject the null hypothesis. This means there is sufficient evidence to conclude that the failure rate is different.

Answer:

B. We should reject $H_0$. There is sufficient evidence to conclude that the failure rate is different.