Answer:
<em>x = 0.05</em>
<em>x = 1.57</em>
Step-by-step explanation:
The given equation is:
Moving all terms to the left side:
Now we define a function:
The solutions of the equation are the values of x such that y=0.
Since the function cannot be solved by algebraic methods, we use a graphing tool.
Those points where the graph crosses the x-axis are solutions of the equation.
Please refer to the graph in the figure below.
We can clearly identify there are two solutions at
x = 0.05
x = 1.57
Using the t-distribution, as we have the standard deviation for the sample, it is found that there is a significant difference between the wait times for the two populations.
<h3>What are the hypothesis tested?</h3>At the null hypothesis, we test if there is no difference, that is:
At the alternative hypothesis, it is tested if there is difference, that is:
For each sample, we have that:
For the distribution of differences, we have that:
It is given by:
In which is the value tested at the null hypothesis.
Hence:
Considering a one-tailed test, as stated in the exercise, with 100 - 1 = 99 df, using a t-distribution calculator, the p-value is of 0.014.
Since the p-value is less than the significance level of 0.05, it is found that there is a significant difference between the wait times for the two populations.
More can be learned about the t-distribution at brainly.com/question/16313918