Question

In: Statistics and Probability

Question 1 Consider the population of history scores for a class comprising 5 students A, B,...

Question 1

Consider the population of history scores for a class comprising 5 students A, B, C, D and, E. The marks are as follows:

Student A B C D E

Score 70 78 80 80 95

(a) List the 10 possible samples of 3 from the 5 students, A, B, C, D and E.

(b) Find the sample mean for each of the 10 samples.

(c) Find the mean of the 10 sample means.

Question 2

Assume that a human pregnancy has a population mean of 280 days and a population standard deviation of 8 days. Determine the following probabilities:

(a) The probability that one randomly chosen pregnant woman exceeds 284 days before giving birth.

(b) We take a random sample of n = 5 pregnant women. Find the probability that the mean number of days for this group of 5 women exceeds 284 days.

(c) Compare your answers for parts a) and b). Why are they different?

(d) What was the value of the standard error for part a)? For part (b)? Why are these different?

Question 3

In a random sample of forty-eight 200-metre swims has a mean time of 3.12 minutes and a standard deviation of 0.09 minutes.

(a) Construct the 89% confidence interval for the population mean time.

(b) If all the other quantities remain the same, how does the indicated change affect the width of the confidence interval?

(i) Increase in the sample size

(ii) Increase in the level of confidence.

Question 4

In a sample of 400 shops it was discovered that 136 of them sold carpets at below the list prices, which had been recommended by manufacturers.

(a) Estimate the percentage of all carpet selling shops below list price.

(b) Calculate the 95% confidence limits for this estimate.

Expert Solution

orchestra answered 2 years ago

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