Use the following information to answer the question. A janitor at a large office building believes that his supply of light
bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p $p = 0.07$ (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05.
Symbolically, the null and alternative hypothesis are as follows: $$\mathrm { H } _ { 0 } : \mathrm { p } = 0.07 \text { and } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } 0.07$$
-Suppose that the janitor tests 300 randomly selected light bulbs and finds that 27 bulbs are defective. What value of the test statistic should he report? Round to the nearest hundredth.
A) $z = - 1.96$
B) $z = 1.96$
C) $z = 1.36$
D) $z = - 1.36$

Question

Use the following information to answer the question. A janitor at a large office building believes that his supply of light
bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p $p = 0.07$ (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05.
Symbolically, the null and alternative hypothesis are as follows: $$\mathrm { H } _ { 0 } : \mathrm { p } = 0.07 \text { and } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.07$$
-Suppose that the janitor tests 300 randomly selected light bulbs and finds that 27 bulbs are defective. What value of the test statistic should he report? Round to the nearest hundredth. 
A) $z = - 1.96$
B) $z = 1.96$
C) $z = 1.36$
D) $z = - 1.36$

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a proportion: $ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} $, where $\hat{p} = \frac{27}{300} = 0.09$, $p_0 = 0.07$, and $n = 300$. Plugging in these values gives $ z = \frac{0.09 - 0.07}{\sqrt{\frac{0.07 \times 0.93}{300}}} \approx 1.36 $.

Use the Following Information to Answer the Question p=0.07p = 0.07p=0.07

Use the Following Information to Answer the Question $p = 0.07$