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Answer:
Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%.
Step-by-step explanation:
In this case we need to test whether the popular charity has expenses that are higher than other similar charities.
The hypothesis for the test can be defined as follows:
<em>H</em>₀: The popular charity has expenses that are higher than other similar charities, i.e. <em>μ </em>> 0.31.
<em>Hₐ</em>: The popular charity has expenses that are less than other similar charities, i.e. <em>μ </em>< 0.31.
As the population standard deviation is not known we will use a t-test for single mean.
Compute the sample mean and standard deviation as follows:
Compute the test statistic value as follows:
Thus, the test statistic value is -2.62.
Compute the p-value of the test as follows:
*Use a t-table.
Thus, the p-value of the test is 0.014.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.014 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Thus, concluding that there is sufficient evidence to conclude that the mean is less than 31%.
Answer:
C)
Step-by-step explanation:
Recall the Pythagorean Trigonometric Identity where , so