A city ordinance requires that a smoke detector be installed in all residential housing. There is concern that too many residences are still without detectors, so a costly inspection program is being contemplated. Let p be the proportion of all residences that have a detector. A random sample of 25 residences is selected. If the sample strongly suggests that p < 0.80 (less than 80% have detectors), as opposed to p ≥ 0.80, the program will be implemented. Let x be the number of residences among the 25 that have a detector, and consider the following decision rule: Reject the claim that p = 0.8 and implement the program if x ≤ 15. (Round your answers to three decimal places.) a.)What is the probability that the program is implemented when p = 0.80? b.)What is the probability that the program is not implemented if p = 0.60?

When two births are randomly selected, the sample space for genders is bb, bg. gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is , and this is not affected by how many boys or girls have previously been born. 2 Determine the probabilities of each sample proportion. Probability Sample proportion of girls Tune intanare or cimnlifiad frartinne

The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. A) find the mean of p b)find the standard deviation of p c)Compute an approximation for P≥p0.0125, which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.

The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service.   The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p.   (b) Find the standard deviation of p.   (c) Compute an approximation for P(P ≥ 0.0125), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.

Suppose that a set of ten measurements is drawn randomly. The sample consists of the set {1,1,0,15,2,3,4,0,1,3}. By inspection it is evident that the measurement x=15 appears unusually large in comparison to the rest of the measurements. Calculate the z-score equivalent for the measurement x=15 and determine if it is an outlier.

At ABC College it is estimated that at most 10% of the students use public transportation to the college. Does it seem to be a valid estimate if, in a random sample of 120 students, 25 students use public transportation. (Use α = .01)

Suppose that 67% of voters in a state oppose concealed carry handguns. Repeated random samples of 400 voters were collected. Use the Empirical Rule to find the interval in which the sample proportion of opponents should fall 95% of the time. Select one: A. (64.6%,69.4%)(64.6%,69.4%) B. (63.8%,70.2%)(63.8%,70.2%) C. (60.7%,73.3%)(60.7%,73.3%) D. (61.5%,72.5%)(61.5%,72.5%) E. None of the above

A transect is an archaeological study area that is  mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance . In a different section of Chaco Canyon, a random sample of 23 transects gave a sample variance  for the number of sites per transect. Use an  to test the claim that the variance in the new section is greater than 36.4.​ What is the level of significance?   90%   1%   5%   95%   10%

The single sample z test may be used to determine:   a)the variability in the sample b)if a sample mean is different from a known population mean c)if two population means are different d)the variability in the population of sample means

6% of all statistics classes require a statistical calculator and 25% require the use of a computer that has statistical software. Of the classes that require a statistical calculator, 13% also require the use of a computer. If a statistics course is selected at random find: (round to 4 decimal places where possible) a.  P(Statistical Calculator) = Correct b. P(Statistical Software) = Correct c. P(Require a Statistical Calculator and Statistical Software) = Incorrect d. P(Require a Statistical Calculator GIVEN Require Statistical Software) =