Historically it has been observed that patients admitted to a certain hospital for treatment of influenza spend a MEAN length of 4.4 days in the hospital. Every flu season, different strains of the flu circulate: Some years the primary strain causes more severe illness (and presumably longer than average hospital stays) and other years less so (meaning presumably shorter than average stays). We assume the hospital stays are NORMALLY distributed. a. A hospital wants to see how this year's flu season compares to previous years. Therefore, state the null and alternate hypotheses that would be used to test whether the hospital is seeing a mean hospital stay that is significantly DIFFERENT than the historical mean of 4.4 days. b. FIFTEEN patients admitted for influenza treatment are then randomly sampled and the length of their hospital stay in days is given below. 4641056443743774 SAMPLE MEAN =? SAMPLE STANDARD DEVIATION =? c. Using the results of part (b), determine what type of test is suitable, and then find the p-value of the appropriate hypothesis test. Type of Test is:? p-value=? Use part b to construct a 95% CONFIDENCE INTERVAL for the MEAN number of days patients hospitalized for flu treatment spend in the hospital. ( KEEP 3 DECIMALS please). lower limit=? , upper limit=? Using part (c), decide whether or not to reject the null hypothesis at the 5% significance level. Your conclusion at 5% significance level is:? What TYPE OF ERROR is possible with your final decision about the null hypothesis in part above?

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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Historically it has been observed that patients admitted to a certain hospital for treatment of influenza spend a MEAN length of 4.4 days in the hospital. Every flu season, different strains of the flu circulate: Some years the primary strain causes more severe illness (and presumably longer than average hospital stays) and other years less so (meaning presumably shorter than average stays). We assume the hospital stays are NORMALLY distributed.

a. A hospital wants to see how this year's flu season compares to previous years. Therefore, state the null and alternate hypotheses that would be used to test whether the hospital is seeing a mean hospital stay that is significantly DIFFERENT than the historical mean of 4.4 days.

b. FIFTEEN patients admitted for influenza treatment are then randomly sampled and the length of their hospital stay in days is given below.

4641056443743774

SAMPLE MEAN =?

SAMPLE STANDARD DEVIATION =?

c. Using the results of part (b), determine what type of test is suitable, and then find the p-value of the appropriate hypothesis test.

Type of Test is:?

p-value=?

Use part b to construct a 95% CONFIDENCE INTERVAL for the MEAN number of days patients hospitalized for flu treatment spend in the hospital. ( KEEP 3 DECIMALS please).

lower limit=? , upper limit=?

Using part (c), decide whether or not to reject the null hypothesis at the 5% significance level.

Your conclusion at 5% significance level is:?

What TYPE OF ERROR is possible with your final decision about the null hypothesis in part above?

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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