10. Suppose the number of beds filler per day in a medium-sized hospital is normally distributed. A hospital administrator tells the board of directors that, on the average, at least 185 beds are filled on any given day. One of the board members believes this figure is inflated, and she manages to secure a random sample of figures for 16 days. The data are shown here. Use a=.025 and the sample data to test whether the hospital administrator's statement is false. Assume the number of filled beds per day is normally distributed. Select the appropriate hypothesis test and complete the analysis using critical values and confirm using p-values. Number of Beds Occupied per Day:
173 149 166 180
189 170 152 194
177 169 188 160
199 175 172 187
a.)
Level of Significance 0.0250
Sample Size 16.0000
Sample Mean 175.0000
Sample Standard Deviation 14.2829
Intermediate Calculations
Standard Error of the Mean 3.5707
Degrees of Freedom 15.0000
t Test Statistic -2.8006
One-Tail Test
Critical Value 2.1314
p-Value 0.0067
Two-Tail Test
Critical Value 2.4899
p-Value 0.0134
b.)
Level of Significance 0.0250
Population Standard Deviation 14.2829
Sample Size 16.0000
Sample Mean 175.0000
Intermediate Calculations
Standard Error of the Mean 3.5707
Z Test Statistic -2.8006
Two-Tail Test
Lower Critical Value 2.2414
p-Value 0.0051
One-Tail Test
Critical Value 1.9600
p-Value 0.0026