An article describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from soil. Out of 155 seeds planted in soil containing 3% mushroom compost by weight, 74 germinated. Out of 155 seeds planted in soil containing 5% mushroom compost by weight, 86 germinated. Can you conclude that the proportion of seeds that germinate differs with the percent of mushroom compost in the soil

Solution :

Let and  represents the proportions of the seeds which germinate among the seeds planted in the soil containing and mushroom compost by weight respectively.

To test the null hypothesis against the alternate hypothesis   .

Let denotes the respective sample proportions and the represents the sample size respectively.

The test statistic can be written as :

which under  follows the standard normal distribution.

We reject at level of significance, if the P-value or if

Now, the value of the test statistics = -1.368928

The critical value =

P-value =

                                     = 0.171335

Since the p-value > 0.05 and , so we fail to reject at level of significance.

Hence we conclude that the two population proportion are not significantly different.

Conclusion :

There is not sufficient evidence to conclude that the of the seeds that with the percent of the in the soil.

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled