Which of the following statements are true? Check all that apply.
1 answer:
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The exponential functions change is represented by decay and the percentage rate of decrease is 1.00619%.
Step-by-step explanation:
Step 1:
To determine if the function represents growth or decay, we substitute values to x.
If the values increase with an increase of x, it represents growth.
If the values decrease with an increase of x, it represents decay.
Step 2:
If
If
So as x increases the value of y decreases, so it represents decay.
Step 3:
The percentage rate of change is determined by dividing the difference of two consecutive values by the first value.
The percentage rate of change
Substituting the values, we get
The percentage rate of change .
As the values of y decrease with an increase in x, it is the percent decrease per unit.
Answer:
Since is a bilateral test the p value would be:
Comparing the p value with the significance level given we see that
so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.
Step-by-step explanation:
Data given and notation
represent the sample mean for Atlanta
represent the sample mean for Chicago
represent the sample deviation for Atlanta
represent the sample standard deviation for Chicago
sample size for the group Atlanta
sample size for the group Chicago
t would represent the statistic (variable of interest)
significance level provided
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the meanfor atlanta is different from the mean of Chicago, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:
(1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the value of the test statistic for this hypothesis testing.
Since we have all the values we can replace in formula (1) like this:
What is the p-value for this hypothesis test?
The degrees of freedom are given by:
Since is a bilateral test the p value would be:
Based on the p-value, what is your conclusion?
Comparing the p value with the significance level given we see that
so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.