An ordinance requiring that a smoke detector be installed in all previously constructed houses has been in effect in a particular city for one year. The fire department is concerned that many houses remain without detectors. Let p = the true proportion of such houses having detectors and suppose that a random sample of 25 homes is inspected. If the sample strongly indicates that fewer than 80% of all houses have a detector, the fire department will campaign for a mandatory inspection program. Because of the costliness of the program, the department prefers not to call for such inspections unless sample evidence strongly argues for their necessity. Let X denote the number of homes with detectors among the 25 sampled. Consider rejecting the claim that p > .8 if x < 15, where x is the observed value of X.
a) what is the probability that the claim is rejected when the actual value of p is .8?
b) what is the probability of not rejecting the claim when the actual value of p is .8?
c) how do the error probabilities of parts (a) and (b) change if the value 15 in the decision rule is replaced by 14?

a. P=0.01222

b. P=0.98778

c. The probability of rejecting the claim is now P=0.00298.

Step-by-step explanation:

In this case, we evaluate the sampling distribution for a population proportion π=0.8 with a sample size of 25.

We need to calculate the probability of getting a sample mean below 15, which means p=15/25=0.6.

The standard deviation of the sampling distribution is:

The z value por p=0.6 is

The probability of having a sample mean less than 15 is

The probaiblity of not rejecting the claim is 1-0.01222=0.98778

If the value 15 is replaced by 14, we have a new value of p=14/25=0.56.

There will be less chances of rejecting the hypothesis.

y= -

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.