8.1

Classify the two given samples as independent or dependent.

Sample 1: The scores of 22 students who took the ACT Sample 2: The scores of 22 different students who took the SAT

• Dependent

• Independent

• No relationship

• None of these

As part of a Masterʹs thesis project, a mathematics teacher is interested in the effects of two different teaching methods on mathematics achievement. She randomly chooses a class of students to learn one algebraic concept using traditional methods. Then on another day, the same students learn a similar algebraic concept using manipulatives. The teacher then compares their test scores. Determine whether the samples are dependent or independent.

• No relationship

• Independent

• Dependent

• None of these

Find the standardized test statistic to test the claim that μ1 =μ2. Assume the two samples are random and independent.

Population statistics: σ1 = 2.5 and σ2 = 2.8

Sample statistics: x1 = 3, n1 = 40 and x2 = 4, n2 = 35

• -0.8

• -1.6

• -2.6

• -1.0

Find the standardized test statistic to test the claim that μ1 >μ2. Assume the two samples are random and independent.

Population statistics: σ1 = 45 and σ2 = 25

Sample statistics: x1 = 480, n1 = 100 and x2 = 465, n2 = 125

• 0.91

• 1.86

• 2.81

• 2.99

Suppose you want to test the claim that μ1 =μ2. Assume the two samples are random and independent. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

• There is sufficient evidence to reject the claim μ1 =μ2.

• There is not sufficient evidence to reject the claim μ1 =μ2.

• There is sufficient evidence to support the claim μ1 =μ2.

• There is not sufficient evidence to support the claim μ1 =μ2.

Suppose you want to test the claim that μ1 >μ2. Assume the two samples are random and independent. At a level of significance of α = 0.01, should you reject the null or fail to reject the null?

Population statistics: σ1 = 45 and σ2 = 25

Sample statistics: x1 = 805, n1 = 100 and x2 = 790, n2 = 125

• Reject Ho, there is enough evidence to REJECT the claim.

• Reject Ho, there is enough evidence to SUPPORT the claim.

• Fail to reject Ho, there is NOT enough evidence to SUPPORT the claim.

• Fail to reject Ho, there is NOT enough evidence to REJECT the claim.

Two samples are random and independent. Find the P-value used to test the claim that μ1 = μ2. Use α=0.05.

Population statistics: σ1 = 2.5 and σ2 = 2.8

Sample statistics: x1 = 12, n1 = 40 and x2 = 13, n2 = 35

• p = 0.213

• p = 0.621

• p = 0.105

• p = 0.402

Test the claim that μ1 < μ2. Assume the two samples are random and independent. Use α = 0.05.

Population statistics: σ1 = 3.1 and σ2 = 2.95

Sample statistics: x1 = 25.6, n1 = 35 and x2 = 28.15, n2 = 42

• Reject Ho, there is enough evidence to REJECT the claim.

• Fail to reject Ho, there is NOT enough evidence to SUPPORT the claim.

• Reject Ho, there is enough evidence to SUPPORT the claim.

• Fail to reject Ho, there is NOT enough evidence to REJECT the claim.

A medical researcher suspects that the pulse rate of smokers is higher than the pulse rate of non-smokers. Test the researcherʹs suspicion using α = 0.005. Assume the two samples are random and independent.

• Reject Ho, there is enough evidence to SUPPORT the claim.

• Fail to reject Ho, there is NOT enough evidence to SUPPORT the claim.

• Fail to reject Ho, there is NOT enough evidence to REJECT the claim

• Reject Ho, there is enough evidence to REJECT the claim.

Two samples are random and independent. Find the P-value used to test the claim that μ1 = μ2. Use α=0.05.

Population statistics: σ1 = 5 and σ2 = 8

Sample statistics: x1 = 24, n1 = 100 and x2 = 23, n2 = 120

• p = 0.211

• p = 0.621

• p = 0.105

• p = 0.259