Question

The U.S. Federal Seed Act establishes germination rates for various fruit and vegetable seeds. Watermelon seeds are to meet a 70% germination standard. A skeptical gardener who has not had very good luck planting watermelons believes that the seed company he purchases seeds from is not adhering to the 70% federal mandate. Once a week for 12 weeks, he purchases a pack of 10 watermelon seeds to act as his sample. He plants the seeds in a greenhouse with good soil to maintain a consistent temperature and watering routine. He finds that the germination rate for the company's watermelon seeds is 55%. Is this convincing evidence that the proportion of watermelon seeds that germinate is less than 70%

Answer 1

Answer:

Following are the responses to the given question:

Step-by-step explanation:

Level of Significance,$\alpha = 0.05$

Sample Size, $n = 120$          

Sample Proportion,   $\hat{P} = 0.600$      

$z -value = Z_{\frac{\alpha}{2}} = 1.960 \ \ [excel formula =NORMSINV(\frac{\alpha}{2})]$

Standard Error$SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = 0.0447$        

margin of error $E = Z\times SE = 1.960 \times 0.0447 = 0.0877$

When $95\%$ Confidence Interval              

Interval Lower Limit$= \hat{p} - E = 0.600 - 0.0877 = 0.5123$

Interval Upper Limit $=\hat{p}+ E = 0.600 + 0.0877 = 0.6877$