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Answer :
Final answer:
Based on the sample data and the calculated t-value, there is sufficient evidence at the 0.05 level of significance to conclude that the average yield of coffee trees is different from 179 lb.
Explanation:
To determine whether there is sufficient evidence to conclude that the average yield of coffee trees is 179 lb, we need to perform a hypothesis test. The null hypothesis (H0) is that the average yield is 179 lb, and the alternative hypothesis (Ha) is that the average yield is different from 179 lb.
We can use the t-test for a sample mean to test this hypothesis. The formula for the t-test statistic is:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is the average yield of the 5 trees, which is calculated as (155 + 185 + 175 + 214 + 199) / 5 = 185.6 lb. The population mean is 179 lb. The sample standard deviation can be calculated using the formula:
sample standard deviation = sqrt(sum((x - sample mean)^2) / (sample size - 1))
After calculating the sample standard deviation, we can substitute the values into the t-test formula to calculate the t-value.
If the calculated t-value is greater than the critical t-value of 2.766 (at the 0.05 level of significance), we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the average yield is different from 179 lb. Otherwise, we fail to reject the null hypothesis.
Learn more about hypothesis testing here:
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