Estimation & Hypothesis Testing for Two Population Parameters

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Assignment

(32 points due by 11 pm December 3rd)

Note: You can team up with one of your classmates to complete the assignment (not more than two in a team); if you want to work on the assignment individually, that’s also fine. If you are working in teams, then only one submission is required per team; include both the team members’ last names as part of the assignment submission file name as well as in the assignment submission document.

Please provide detailed solutions to the following problems/exercises (4 problems/exercises x 8 points each):

1) A marketing analyst would like to have two brands of tea packs rated by consumers.

a) Explain how the marketing analyst can use dependent samples to collect the data.

b) Explain how the marketing analyst can use independent samples to collect the data.

2) A random sample results in 1 = 20 with n1 = 100. The population standard deviation is σ1 = 6. Another sample was selected independently resulting in 2 = 22 with n2 = 100. The population standard deviation is σ2 = 7. Test that the population means differ using a 1% significance level.

3) The supervisor of a hardware manufacturer is conducting a test of the tensile strengths of steel coils. He obtained the following data: Coil 1: = 118, s – 17, n -9, and Coil 2: = 143, s = 24, n = 16. The tensile strength for the two types of steel coils are approximately normally distributed. Based on the p value, do the data support the conclusion that the mean tensile strengths of the two coils are different at a significance level of 7%? Do not assume that the population variances are equal.

4) Twenty mortgage firms were selected and the amount of mortgage financing was recorded for 2010 and 2011. If the mean difference was $5.434 million with the standard deviation of the differences being $8.764 million, is there sufficient evidence to support that a difference exists in the amount of mortgage refinancing for 2010 and 2011? Use a 1% significance level.

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