Nationally, patients who go to the emergency room wait an average of 5 hours to be admitted into the hospital. Do patients at rural hospitals have a higher waiting time? The 15 randomly selected patients who went to the emergency room at rural hospitals waited an average of 7.2 hours to be admitted into the hospital. The standard deviation for these 15 patients was 2.9 hours. What can be concluded at the the αα = 0.01 level of significance level of significance? For this study, we should use Select an answer= z-test for a population proportion or t-test for a population mean The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer ≠ < = > H1:H1: ? μ p Select an answer ≠ < = > The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer reject accept fail to reject the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly higher than 5 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 5 hours. The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly higher than 5 hours at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is higher than 5 hours. The data suggest the populaton mean is significantly higher than 5 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is higher than 5 hours.

Nationally, patients who go to the emergency room wait an average of 5 hours to be admitted into the hospital. Do patients at rural hospitals have a higher waiting time? The 15 randomly selected patients who went to the emergency room at rural hospitals waited an average of 7.2 hours to be admitted into the hospital. The standard deviation for these 15 patients was 2.9 hours. What can be concluded at the the αα = 0.01 level of significance level of significance? For this study, we should use Select an answer= z-test for a population proportion or t-test for a population mean The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer ≠ < = > H1:H1: ? μ p Select an answer ≠ < = > The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer reject accept fail to reject the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly higher than 5 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 5 hours. The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly higher than 5 hours at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is higher than 5 hours. The data suggest the populaton mean is significantly higher than 5 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is higher than 5 hours.

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Description: Nationally, patients who go to the emergency room wait an average of 5 hours to be admitted into the hospital. Do patients at rural hospitals have a higher waiting time? The 15 randomly selected patients who went to the emergency room at rural hospit

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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For this study, we should use Select an answer= z-test for a population proportion or t-test for a population mean
The null and alternative hypotheses would be:

H0:H0: ? μ p Select an answer ≠ < = >

H1:H1: ? μ p Select an answer ≠ < = >

The test statistic ? t z = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is ? > ≤ αα
Based on this, we should Select an answer reject accept fail to reject the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the population mean is not significantly higher than 5 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 5 hours.
- The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly higher than 5 hours at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is higher than 5 hours.
- The data suggest the populaton mean is significantly higher than 5 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is higher than 5 hours.

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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Step 1

Given that,

The 15 randomly selected patients who went to the emergency room at rural hospitals waited an average of 7.2 hours to be admitted into the hospital. The standard deviation for these 15 patients was 2.9 hours.

Step 2

1. For this study, we should use t-test for a population mean

2. Hypothesis:

$H_{0} : μ = 5$

$H_{1} : μ > 5$

Test statistic:

$\begin{array}{rcl} t & = & \frac{\bar{x} - μ}{\frac{s}{\sqrt{n}}} \\ = & \frac{7.2 - 5}{\frac{2.9}{\sqrt{15}}} \\ = & 2.938 \end{array}$

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