A hospital administrator tells
A hospital administrator tells the board of directors that, onaverage, at least 185 beds are filled on any given day. One of theboard members believes this figure is inflated and manages tosecure a random sample of occupancy figures for 16 days. The datais given below and in the Excel file Ass3_Q3a.xlsx. (i) Use thesample data and a significance level of 0.01 to carry out ahypothesis test to test the administrator’s claim. Assume thenumber of beds filled per day is Normally distributed in thepopulation. (ii) Explain, in words, the meaning of a type I and atype II error in this situation. (iii) Write down, in a fewsentences, the consequences for the hospital for making each ofthese two statistical errors.
data:
| # beds occupied per day | |
| 173 | |
| 189 | |
| 177 | |
| 199 | |
| 149 | |
| 170 | |
| 169 | |
| 175 | |
| 166 | |
| 152 | |
| 188 | |
| 172 | |
| 180 | |
| 194 | |
| 160 | |
| 187 | |
Answer:
Hypotheses are:
Following is the output of single sample t test:
| Hypothesis Test: Mean vs. Hypothesized Value | ||||||
| 185.000 | hypothesized value | |||||
| 175.000 | mean #beds occupied per day | |||||
| 14.283 | std.dev. | |||||
| 3.571 | std.error | |||||
| 16 | n | |||||
| 15 | df | |||||
| -2.80 | t | |||||
| .0067 | p-value(one-tailed, lower) | |||||
Since p-value is less than 0.01 so we reject the nullhypothesis. That is we cannot conclude that at least 185 beds arefilled on any given day.
(ii)
Type I error is the probability of rejecting the true nullhypothesis.
That is researcher incorrectly conclude that averagely less than185 beds filled while actually at least 185 beds are filled on anygiven day.
Type II error is the probability of fail to reject the true nullhypothesis.
That is researcher incorrectly conclude that averagely at least185 beds are filled on any given day while it is less than 185 bedsare filled on any given day.
(iii)
In case of type I error board of director may not take necessarysteps to increase facilities in hospital, while these steps shouldbe take.
In case of type II error board of director may take necessarysteps to increase facilities in hospital, while these steps shouldnot be taken.
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