The waiting time of patients in different states can be found via https://projects.propublica.org/emergency/Problem 3. Georgia claims that it has a lower average (mean) emergency room waiting time compared with South Carolina. Use this dataset to test this hypothesis with the confidence of 95%. (Hint: You need to test the variance equality first).Problem 4. Use the Georgia waiting time data to define and test a two-population hypothesis test. Establish your hypothesis, test it and check whether reject or not for both questions. important inormation will be found on the link above. Also I have attached helpful information to answer the question. R# Perform two-sample t-test assuming equal variancest_test<- t.test(waiting times_georgia, waiting times_south_carolina, var.equal = TRUE)t_testProblem 4:To define and test a two-population hypothesis test for Georgia's waiting time data, we can set up thefollowing hypotheses:Null hypothesis: The average waiting time in Georgia is equal to a specific value (e.g., 40 minutes)Alternative hypothesis: The average waiting time in Georgia is not equal to the specific valueWe can conduct a one-sample t-test in R to test this hypothesis:R#Load the Georgia waiting time datawaiting times_georgia <- c(45, 30, 50, 40, 35)#Perform one-sample t-testt_test_georgia <- t.test(waiting times_georgia, mu= =40)t_test_georgia THE ANSWER IS IN THE EXPLANATION SECTION BELOWExplanation:Problem 3:We must use an F-test to check for equality of variances before comparing the average ER wait times inGeorgia and South Carolina.Null hypothesis: There is no difference in waiting times between South Carolina and Georgia.Hypothesis alternative: There is a difference in waiting times between Georgia and South Carolina.We can conduct an F-test in R using the var.test function:R# Load the datawaiting times_georgia <- c(45, 30, 50, 40, 35)waiting times_south_carolina <- c(50, 40, 55, 45, 42)# Perform the F-testvar_test <-var.test(waiting times_georgia, waiting times_south_carolina)var_testIf the result of the F-test indicates that the variances are not significantly different, we can proceed with atwo-sample t-test to compare the means of waiting times in Georgia and South Carolina:

Given the data asWaiting TimesGeorgiaSouth Carolina45503040505540453542

Answered: The waiting time of patients in…

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Question

The waiting time of patients in different states can be found via https://projects.propublica.org/emergency/

Problem 3. Georgia claims that it has a lower average (mean) emergency room waiting time compared with South Carolina. Use this dataset to test this hypothesis with the confidence of 95%. (Hint: You need to test the variance equality first).

Problem 4. Use the Georgia waiting time data to define and test a two-population hypothesis test.

Establish your hypothesis, test it and check whether reject or not for both questions. important inormation will be found on the link above. Also I have attached helpful information to answer the question.

R
# Perform two-sample t-test assuming equal variances
t_test<- t.test(waiting times_georgia, waiting times_south_carolina, var.equal = TRUE)
t_test
Problem 4:
To define and test a two-population hypothesis test for Georgia's waiting time data, we can set up the
following hypotheses:
Null hypothesis: The average waiting time in Georgia is equal to a specific value (e.g., 40 minutes)
Alternative hypothesis: The average waiting time in Georgia is not equal to the specific value
We can conduct a one-sample t-test in R to test this hypothesis:
R
#Load the Georgia waiting time data
waiting times_georgia <- c(45, 30, 50, 40, 35)
#Perform one-sample t-test
t_test_georgia <- t.test(waiting times_georgia, mu= =40)
t_test_georgia

THE ANSWER IS IN THE EXPLANATION SECTION BELOW
Explanation:
Problem 3:
We must use an F-test to check for equality of variances before comparing the average ER wait times in
Georgia and South Carolina.
Null hypothesis: There is no difference in waiting times between South Carolina and Georgia.
Hypothesis alternative: There is a difference in waiting times between Georgia and South Carolina.
We can conduct an F-test in R using the var.test function:
R
# Load the data
waiting times_georgia <- c(45, 30, 50, 40, 35)
waiting times_south_carolina <- c(50, 40, 55, 45, 42)
# Perform the F-test
var_test <-var.test(waiting times_georgia, waiting times_south_carolina)
var_test
If the result of the F-test indicates that the variances are not significantly different, we can proceed with a
two-sample t-test to compare the means of waiting times in Georgia and South Carolina:

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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