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Question

asked 2021-08-08

At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you expect to find in a typical cluster? With what standard deviation?

asked 2021-08-20

The mean time to sell a residential property in the area is 60 days.

You select a random sample of 20 homes sold in the last year and find the mean selling time is 65 days with a standard deviation of 9 days.

Based on the data, develop a 95 percent confidence interval for the population mean.

You select a random sample of 20 homes sold in the last year and find the mean selling time is 65 days with a standard deviation of 9 days.

Based on the data, develop a 95 percent confidence interval for the population mean.

asked 2021-08-22

The gross weekly sales at a certain restaurant is a normal random variable with mean $2200 and standard deviation $230.

What is the probability that

(a) the total gross sales over the next 2 weeks exceeds $5000.

(b) weekly sales exceed $2000 in at least 2 of the next 3 weeks? What independence assumptions have you made?

What is the probability that

(a) the total gross sales over the next 2 weeks exceeds $5000.

(b) weekly sales exceed $2000 in at least 2 of the next 3 weeks? What independence assumptions have you made?

asked 2021-05-14

When σ is unknown and the sample size is \(\displaystyle{n}\geq{30}\), there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When \(\displaystyle{n}\geq{30}\), use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?