Question

A hospital administrator tells the board of directors that, on average, at least 185 beds are filled on any given day. One of the board members believes this figure is inflated and manages to secure a random sample of occupancy figures for 16 days. The data is given below and in the Excel file Ass3_Q3a.xlsx. (i) Use the sample data and a significance level of 0.01 to carry out a hypothesis test to test the administrator’s claim. Assume the number of beds filled per day is Normally distributed in the population. (ii) Explain, in words, the meaning of a type I and a type II error in this situation. (iii) Write down, in a few sentences, the consequences for the hospital for making each of these 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 1

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 null hypothesis. That is we cannot conclude that at least 185 beds are filled on any given day.

(ii)

Type I error is the probability of rejecting the true null hypothesis.

That is researcher incorrectly conclude that averagely less than 185 beds filled while actually at least 185 beds are filled on any given day.

Type II error is the probability of fail to reject the true null hypothesis.

That is researcher incorrectly conclude that averagely at least 185 beds are filled on any given day while it is less than 185 beds are filled on any given day.

(iii)

In case of type I error board of director may not take necessary steps to increase facilities in hospital, while these steps should be take.

In case of type II error board of director may take necessary steps to increase facilities in hospital, while these steps should not be taken.