An administrator at a hospital claims that an average of 185 beds are occupied each day. A board member believes that the number is inflated and gets data for 16 days. The null hypothesis is the mu=185 and the alternative hypothesis is mu!=185.
(1) A Type II error occurs when a false null hypothesis is accepted. In this situation, if the average number of beds is not 185 ( and from the data given it...
An administrator at a hospital claims that an average of 185 beds are occupied each day. A board member believes that the number is inflated and gets data for 16 days. The null hypothesis is the mu=185 and the alternative hypothesis is mu!=185.
(1) A Type II error occurs when a false null hypothesis is accepted. In this situation, if the average number of beds is not 185 ( and from the data given it appears to be less than 185) but the test does not reject the null hypothesis this would be a Type II error.
If you believed that you needed, on average, 185 beds when you actually needed fewer you might incur additional costs (including staffing for nurses, custodial work, etc...) You might also approve an additional wing which would prove unnecessary.
(2) A Type I error occurs when a true null hypothesis is rejected. In this case, if the average really was 185 but the data indicated that you should reject the null hypothesis a Type I error would occur. (If the board member "cherry picked" the data for unusually slow days this could easily occur -- more difficult to happen by chance. The probability that this happens by chance is restricted by the significance level of the test.)
If you reject the claim that you need 185 beds, when you actually do, you might find yourself understaffed or unable to accommodate your patients.
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