Nationally, patients who go to the emergency room wait an average of 6 hours to be admitted into the hospital. Do patients at rural hospitals have a lower waiting time? The 12 randomly selected patients who went to the emergency room at rural hospitals waited an average of 4.7 hours to be admitted into the hospital. The standard deviation for these 12 patients was 2.3 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 t-test for a population mean The null and alternative hypotheses would be: H0:H0: ? p μ Select an answer = > ≠ < H1:H1: ? p μ Select an answer = ≠ > < The test statistic ? z t = (please show your answer to 2 decimal places.)The p-value = (Please show your answer to 4 decimal places.)The p-value is ? ≤ > ααBased on this, we should Select an answer accept reject fail to reject the null hypothesis.

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Nationally, patients who go to the emergency room wait an average of 6 hours to be admitted into the hospital. Do patients at rural hospitals have a lower waiting time? The 12 randomly selected patients who went to the emergency room at rural hospitals waited an average of 4.7 hours to be admitted into the hospital. The standard deviation for these 12 patients was 2.3 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 t-test for a population mean
The null and alternative hypotheses would be:

H0:H0: ? p μ Select an answer = > ≠ <

H1:H1: ? p μ Select an answer = ≠ > <

The test statistic ? z t = (please show your answer to 2 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 accept reject fail to reject the null hypothesis.

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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The 12 randomly selected patients who went to the emergency room at rural hospitals waited an average of 4.7 hours to be admitted into the hospital and standard deviation is 2.3. That is, $n = 12, \bar{x} = 4.7, s = 2.3$ .

The sample size is less than 30 and the population standard deviation is unknown indicates that the t-test for a population mean is used.

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

Let $μ$ denotes the population mean of waiting time.

The claim of the test is the patients at rural hospitals have a lower waiting time. The population mean is 6 hours.

The hypothesis is,

Null hypothesis:

$H_{0} : μ = 6$

Alternative hypothesis:

$H_{1} : μ < 6$

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