Hospital Readmission A hospital readmission is an episode when a patient who has been discharged from a hospital is readmitted again within a certain period. Nationally the readmission rate for patients with pneumonia is 17 % . A hospital was interested in knowing whether their readmission rate for pneumonia was less than the national percentage. They found 11 patients out of 70 treated for pneumonia in a two-month period were readmitted. a. What is p ^ , the sample proportion of readmission? b. Write the null and alternative hypotheses. c. Find the value of the test statistic and explain it in context. d. The p-value associated with this test statistic is 0.39. Explain the meaning of the p-value in this context. Based on this result, does the p-value indicate the null hypothesis should be doubted?
Hospital Readmission A hospital readmission is an episode when a patient who has been discharged from a hospital is readmitted again within a certain period. Nationally the readmission rate for patients with pneumonia is 17 % . A hospital was interested in knowing whether their readmission rate for pneumonia was less than the national percentage. They found 11 patients out of 70 treated for pneumonia in a two-month period were readmitted. a. What is p ^ , the sample proportion of readmission? b. Write the null and alternative hypotheses. c. Find the value of the test statistic and explain it in context. d. The p-value associated with this test statistic is 0.39. Explain the meaning of the p-value in this context. Based on this result, does the p-value indicate the null hypothesis should be doubted?
Solution Summary: The author explains the null and alternative hypotheses for determining the readmission rate of the hospital.
Hospital Readmission A hospital readmission is an episode when a patient who has been discharged from a hospital is readmitted again within a certain period. Nationally the readmission rate for patients with pneumonia is
17
%
.
A hospital was interested in knowing whether their readmission rate for pneumonia was less than the national percentage. They found 11 patients out of 70 treated for pneumonia in a two-month period were readmitted.
a. What is
p
^
, the sample proportion of readmission?
b. Write the null and alternative hypotheses.
c. Find the value of the test statistic and explain it in context.
d. The p-value associated with this test statistic is
0.39.
Explain the meaning of the p-value in this context. Based on this result, does the p-value indicate the null hypothesis should be doubted?
The average number of minutes Americans commute to work is 27.7 minutes (Sterling's Best Places, April 13, 2012). The average commute time in minutes for 48 cities are as follows:
Click on the datafile logo to reference the data.
DATA file
Albuquerque
23.3
Jacksonville
26.2
Phoenix
28.3
Atlanta
28.3
Kansas City
23.4
Pittsburgh
25.0
Austin
24.6
Las Vegas
28.4
Portland
26.4
Baltimore
32.1
Little Rock
20.1
Providence
23.6
Boston
31.7
Los Angeles
32.2
Richmond
23.4
Charlotte
25.8
Louisville
21.4
Sacramento
25.8
Chicago
38.1
Memphis
23.8
Salt Lake City
20.2
Cincinnati
24.9
Miami
30.7
San Antonio
26.1
Cleveland
26.8
Milwaukee
24.8
San Diego
24.8
Columbus
23.4
Minneapolis
23.6
San Francisco
32.6
Dallas
28.5
Nashville
25.3
San Jose
28.5
Denver
28.1
New Orleans
31.7
Seattle
27.3
Detroit
29.3
New York
43.8
St. Louis
26.8
El Paso
24.4
Oklahoma City
22.0
Tucson
24.0
Fresno
23.0
Orlando
27.1
Tulsa
20.1
Indianapolis
24.8
Philadelphia
34.2
Washington, D.C.
32.8
a. What is the mean commute time for…
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds.
Click on the datafile logo to reference the data.
DATA file
Type of Fund
Domestic Equity
Number of Funds
Total Return (%)
9191
4.65
International Equity
2621
18.15
Hybrid
1419
2900
11.36
6.75
Specialty Stock
a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals)
%
b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
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c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock…
The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided.
Days to
Maturity
20
Dollar Value
($ millions)
20
12
30
7
10
5
6
15
10
Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds (to 1 decimal).
days
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