#1 Test the claim about the difference between two population 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} ; Assume 12= 22

Sample statistics: x₁=2401, s₁=172, n₁=12 and

x₂=2302, s₂=53, n₂=11

(a) Identify the null and alternative hypothesis

(b) T=

(c) P-value =

(d) Decide whether to reject or fail to reject and interpret the decision.

#2 A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World. The results for the samples of customers transactions for the two fast food restaurants are shown below. At =0.01, can you support the magazines claim?

Burger Stop	Fry World
X1 =$9.67	X2 =$9.04
S1= $0.87	S2 = $0.72
n1 = 12	n2= 12

(a) Identify and state H_o and H_{a .}Which hypothesis is the claim?

(b) Find the critical values and identify the rejection region.

(c) Find the standardized test statistics.

(d) Decide whether to reject or fail to reject

(e) Interpret the decision in the context of original claim

#3 Find the equation of regression line for the given data.

Hours spent studying, x	1	1	2	3	5	5
Test score, y	38	43	52	48	61	69

(a) Predict for the value y for x=2.

(b) Predict for the value y for x=4.5.

(c) Predict for the value y for x=15.

(d) Predict for the value y for x=1.5.