The percentage of farmers using fertilizers in Tanzania was known to be 35%. The drought and other
events of the last few years are believed to have had a potential impact on the proportion of farmers
using fertilizers. An international aid program wants to test whether or not the percentage is still around
35% and gathers a random sample of 150 farmers. The findings reveal that 68 of the farmers use
fertilizers. Conduct the test at 5% level of significance and state your conclusion.
To test whether the percentage of farmers using fertilizers is still around 35%, we can use a hypothesis test. The null hypothesis (H0) is that the percentage is still 35%, and the alternative hypothesis (Ha) is that the percentage has changed.
H0: p = 0.35
Ha: p ≠ 0.35
Where p is the true proportion of farmers using fertilizers.
To conduct the test, we need to calculate the test statistic and compare it to the critical value.
The test statistic can be calculated using the formula:
z = (p̂ - p) / √(p(1-p) / n)
Where p̂ is the sample proportion of farmers using fertilizers, p is the population proportion (0.35), and n is the sample size (150).
p̂ = 68/150 = 0.4533
z = (0.4533 - 0.35) / √(0.35(1-0.35) / 150)
= 0.1033 / √(0.2275 / 150)
= 0.1033 / 0.0314
≈ 3.29
The critical value for a two-tailed test at a 5% level of significance is approximately ±1.96. Since the test statistic (3.29) is greater than the critical value (1.96), we can reject the null hypothesis.
Therefore, we have sufficient evidence to conclude that the percentage of farmers using fertilizers in Tanzania has changed from the known 35%.