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

Following are the responses to the given question:

Explanation:

Level of Significance,
`\alpha = 0.05`

Sample Size,
`n = 120`

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

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

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

margin of error
`E = Z* SE = 1.960 * 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`