Statistical Methods — Winter 2018

Construct box plot for the following data: 71, 87, 82, 64, 72, 75, 81, 69, 76, 79, 65, 68, 80, 73, 85, 71, 70, 79, 63, 62, 81, 84, 77, 73, 82, 74, 74, 73, 84, 72, 81, 65, 74, 62, 64, 68, 73, 82, 69, 71

Find out P(B|F), P(G|C) and P(D|F) for the following Data: Events:- Finance =A, Manufacturing =B, Communication = C, Northeast = D, Southeast=E, Midwest = F, West= G Geographic Location Northeast Southeast Midwest West Industry Finance .12 .05 .04 .07 Type Manufacturing .15 .03 .11 .06 Communication .14 .09 .06 .08

List out the characteristics of Binomial Distribution.

Bank customers arrive randomly on weekday afternoons at an average of 3.2 customers every 4 minutes. What is the probability of having more than customers in a 4-minute interval on a weekday afternoon?

Suppose you want to estimate the average age of all Boeing 737-300 airplanes now in active domestic U. S. service. You want to be 95% confident, and you want your estimate to be within one year of the actual figure. The 737-300 was first placed in service about 24 years ago, but you believe that no active 737-300s in the U.S. domestic fleet are more than 20 years old. How large of a sample should you take? OR1

Suppose that during any hour in a large department store, the average number of shoppers is 448, with a standard deviation of 21 shoppers. What is the probability that a random sample of 49 different shopping hours will yield a sample mean between 441 and 446 shoppers?

What is the probability of obtaining a score greater than 750 on a GMAT test that has a mean of 540 and a standard deviation of 100? Assume GMAT scores are normally distributed.

Asurvey of the morning beverage market shows that the primary breakfast beverage for 17% of Americans is milk. Amilk producer in Wisconsin, where milk is plentiful, believes the figure is higher for Wisconsin. To test this idea, she contacts a random sample of 550 Wisconsin residents and asks which primary beverage they consumed for breakfast that day. Suppose 115 replied that milk was the primary beverage. Using a level of significance of .05, test the idea that the milk figure is higher for Wisconsin.

Asample of 87 professional working woman showed that the average amount paid annually into a private pension fund per person was $3352. The population standard deviation is $1100. Asample of 76 professional working men showed that the average amount paid annually into a private pension fund per person was $5727, with a population standard deviation of $1700. Awomen’s activist group wants to “prove” that women do not pay as much per year as men into private pension funds. If they use α=.001 and these sample data, will they be able to reject a null hypothesis that women annually pay the same as or more than men into private pension funds?

Explain random and non random sampling techniques.

Consumers are asked to rate a company both before and after viewing a video on the company twice a day for a week. Use an alpha of .05 to test to determine whether there is a significant increase in the ratings of the company after the one- week video treatment. Assume that differences in rating are normally distributed in the population. Individual 1 2 3 4 5 6 Before 32 11 21 17 30 38 After 39 15 35 13 41 39 22

In a random sample of 1000 persons from town A, 400 are found to be consumers of wheat. In a sample of 800 from town B, 400 are found to be consumers of wheat. Do these data reveal a significant difference between town Aand town B, so far as the proportion of wheat consumers is concerned?

The manufacturer of a certain make of electric bulbs claims that his bulbs have a mean life of 25 months with a standard deviation of 5 months. Arandom sample of 6 such bulbs gave the following values. Life of bulbs: 24, 26, 30, 20, 20, 18 Can you regard the producer’s claim to be valid at 1% level of significance?

Explain Type – Iand Type – II Errors.

For the following Data: X 61 63 67 69 70 74 76 81 86 91 95 97 Y 4.28 4.08 4.42 4.17 4.48 4.30 4.82 4.70 5.11 5.13 5.64 5.562 1) Estimate the Regression Equation. 2) Calculate SSE and coefficient of determination.