Mathematics, 29.11.2019 07:31 AM28

High tech, inc randomly tests its employees about company policies. last year in the 400 random tests conducted, 14 employees failed the test. a. develop a 99% confidence interval for the proportion of applicants that fail the test. (round answers to 3 decimal places) confidence interval for the proportion mean is between and . would it be reasonable to conclude 5% of the employees cannot pass the employee test? yes or no

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Confidence interval for the proportion mean is between 0.0113 and 0.0587. B. Yes, it is reasonable to conclude that 5% of the employees cannot pass the employee test.

Step-by-step explanation:

We have a large sample size of n = 400 random tests conducted. Let p be the true proportion of employees who failed the test. A point estimate of p is $\hat{p} = 14/400 = 0.035$ , we can estimate the standard deviation of $\hat{p}$ as $\sqrt{\hat{p}(1-\hat{p})/n}=\sqrt{0.035(1-0.035)/400}=0.0092$ . A $100(1-\alpha)%$ confidence interval is given by $\hat{p}\pm z_{\alpha/2}\sqrt{\hat{p}(1-\hat{p})/n$ , then, a 99% confidence interval is $0.035\pm z_{0.005}0.0092$ , i.e., $0.035\pm (2.5758)(0.0092)$ , i.e., (0.0113, 0.0587). $z_{0.005} = 2.5758$ is the value that satisfies that there is an area of 0.005 above this and under the standard normal curve. B. Yes, it is reasonable to conclude that 5% of the employees cannot pass the employee test, because this inverval contain 0.05.

Answer from: Quest

3/5

step-by-step explanation:

double number line is not a standard concept, so it must have been defined in your textbook. assume top line is numerator.

Answer from: Quest

1. sometimes

2. never

3 .08c = 7.50+.05c 250 pages

step-by-step explanation:

1. sometimes

the theoretical probability of rolling a 1 is 1/6. perhaps you got really lucky and never rolled a 1 in those 60 times. your experimental probability is 0. or perhaps you rolled a 1 20 times. your experimental probability is 20/60 is 1/3. it really just depends on how you rolled in that experiment.

2. never

the probability of the event occurring is 1. that is being 100 % sure it will happen. that is the maximum amount of confidence we have.

3. no customer card cost: .08 times number of pages

customer card cost: 7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250

the cost is the same at 250 pages

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