The germination rate is the rate at which plants begin to grow after the seed is planted.

Response:

 

   

Thus, the p value calculated came out to be quite small and based on the specified significance level

we can conclude that there is substantial evidence to dismiss the null hypothesis, indicating that at a 5% significance level the germination proportion of seeds is significantly below 0.9 or 90%

Clarification:

Provided data and notation

n=15 indicates the random sample size taken

X=7 indicates the count of seeds that germinated

estimated proportion of seeds that sprouted

indicates the hypothesized value we seek to test

represents the significance level used

z denotes the test statistic (variable under consideration)

signifies the p value (variable under consideration)  

Key concepts and formulas needed  

We will perform a hypothesis test to evaluate the assertion that the true rate of germinated seeds is less than 0.9 or 90%.:  

Null hypothesis:  

Alternative hypothesis:

 

In executing a proportion test, we employ the z statistic given by:  

(1)  The

One-Sample Proportion Test

is utilized to determine if a population proportion

significantly deviates from a proposed value

.

Calculate the test statistic  Since all the necessary information is available, we can substitute into formula (1) like so:  

 

Statistical conclusion  

It's critical to revisit the p value method or p value approach

. "This approach assesses "likely" versus "unlikely" by determining the probability of observing a more extreme test statistic in line with the alternative hypothesis than the one observed, assuming the null hypothesis were true." In simpler terms, it is merely a method to establish a statistical decision on whether to reject or fail to reject the null hypothesis.  

The adopted significance level is . The following step would be to calculate the p value for this analysis.  As it is a left-tailed test, the p value would be:  

 Consequently, the p value shows a very low result and referencing the provided significance level

we can conclude we possess sufficient evidence to reject the null hypothesis, affirming that at the 5% level the proportion of germinated seeds is statistically significantly less than 0.9 or 90%