#1 Test the claim about the difference between two populations means ₁ and ₂ at the level of significance . Assume the samples are random and independent, and the populations are normally distributed.

Claim: _{1 = 2 :} =0.01

Population statistics: ₁= 3.6, ₂=1.7

Sample statistics: x₁=14, n₁=30, x₂=16, n₂=29

(a) Determine the alternative hypothesis

(b) Determine the standardized test statistics.

(c) Determine P-value

(d) Decision

#2 An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average speed is calculated for 60 days in each region. The mean wind speed in Region A is 13.8 miles per hour. Assume the population standard deviation is 2.8 miles per hour. The mean wind speed in Region B is 15.4 miles per hour. Assume the population standard deviation is 3.1 miles per hour. At =0.05, can the company support the researcher's claim?

(a) Identify the claim and state the H_o and H_a

(b) Find the critical values and rejection regions

(c) Find the standardized test statistics z.

(d) Decide whether to reject or fail to reject the null hypothesis and interpret the claim.

#3 H_a: _{1 > 2} , =0.05, n₁=14, n₂=13

(a) Find the critical value(s) assuming that the population variance are equal

(b) Find the critical value(s) assuming the that the population variance are not equal.