Question

Statistics For Business And Economics

Based on a recent census, suppose it is known that the population proportion of Canadians aged 25-64 that have a post-secondary degree is 54%. Interested in testing concepts from your statistics course, suppose that you collect a random sample of Canadians aged 25-64to determine whether your sample results agree with what is known about the population.In your sample of size n = 35, 13 individuals aged 25-64 have a post-secondary degree.

(a) Based on your sample, construct a 95% confidence interval for the true population proportion of individuals in this age group with a post-secondary degree. (Note: this confidence interval will not include the true population value.) You may use geogebra to help out with computations for this problem.

(c) Suppose that it is known with absolute certainty that the true population proportion is 54%, and that your sample was selected using appropriate (simple) random sampling from this entire population. What is the probability that the 95% confidence interval generated from a sample of size n = 35 would contain the true population parameter?

(b) Based on your sample, test the null hypothesis that the population proportion is.54 (against the alternative hypothesis that it is not). Use a significance threshold ofa = 0.05. Indicate whether the results of the test suggest the null hypothesis should be rejected. You may use geogebra to help out with computations for this problem.

(d) Again, it is known with absolute certainty that the true population proportion is 54%,and that your sampling strategy is appropriate for the population. If a hypothesis testis conducted on a sample of size n = 35, with a null hypothesis that the population proportion is .54 and an alternative hypothesis that it is not, and using a significance threshold of a = 0.05, what is the probability that this test will reject the (true) null hypothesis?

(e) You are annoyed that the confidence interval from your sample did not include the true population parameter value. Suppose you were to collect a new sample with n = 1000 instead of n = 35. What is the probability that this new sample will have a confidence interval that includes the true population value?

(f) If the goal of constructing a 95% confidence interval is to estimate the value of the population parameter value, what benefits are there (if any) to increasing the sample size from n = 35 to n = 1000? Hint: think about the "Error Bound of a Proportion(EBP)" value.  Verified   ### Question 45696  Statistics For Business And Economics

(1 point) A biotechnology company produced 182 doses of somatropin, including 12 which were defective. Quality control test 14 samples at random, and rejects the batch if any of the random samples are found defective. What is the probability that the batch gets rejected?

### Question 45695  Statistics For Business And Economics

(1 point) Assume that the monthly worldwide average number of airplaine crashes of commercial airlines is 2.2. What is the probability that there will be
(a) at most 5 such accidents in the next month?
(b) less than 4 such accidents in the next 3 months?
(c) exactly 8 such accidents in the next 5 months?

### Question 45694  Statistics For Business And Economics

(1 point) A certain typing agency employs two typists. The average number of errors per article is 1 when typed by the first typist and 3.2 when typed by the second. If your article is equally likely to be typed by either typist, find the probability that it will have no errors.

### Question 45693  Statistics For Business And Economics

(1 point) The mean number of patients admitted per day to the emergency room of a small hospital is 2. If, on any given day, there are only 7 beds available for new patients,what is the probability that the hospital will not have enough beds to accommodate its newly admitted patients?

### Question 45692  Statistics For Business And Economics

nt) Given that x is a random variable having a Poisson distribution, compute the following:
\text { (a) } P(x=7) \text { when } \mu=0.5
P(x \leq 6) \text { when } \mu=4.5
\text { c) } P(x>3) \text { when } \mu=5.5
P(x<9) \text { when } \mu=4.5

### Question 45691  Statistics For Business And Economics

B. Compute the probability that in the next 8 hours, more than 24 cars will arrive.
A. Determine the probability that over the next hour, only one car will arrive.
Cars arriving for gasoline at a Shell station follow a Poisson distribution with a mean of 9 per hour.

### Question 45690  Statistics For Business And Economics

Complaints about an Internet brokerage firm occur at a rate of 5 per day. The number of complaints appears to be Poisson distributed.
A. Find the probability that the firm receives 4 or more complaints in a day.
Probability =%3D
B. Find the probability that the firm receives 22 or more complaints in a 5-day period.
Probability =

### Question 45689  Statistics For Business And Economics

Flaws in a carpet tend to occur randomly and independently at a rate of one every 150 square feet. What is the probability that a carpet that is 9 feet by 13 feet contains noflaws?
Probability:

### Question 45688  Statistics For Business And Economics

The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.4 per week. Find the probability of the following events.
.4 or more accidents occur in a week.
A. No accidents occur in one week.
One accident occurs today.

### Question 45687  Statistics For Business And Economics

(1 point) An airline company is considering a new policy of booking as many as 271 persons on an airplane that can seat only 260. (Past studies have revealed that only 89%of the booked passengers actually arrive for the flight.) Estimate the probability that if the company books 271 persons. not enough seats will be available.

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