Katie Sr Yr Stats Final set 8 #2 (problem 15)

A hiking gear company wants to know whether their new hiking boots provide better comfort than their old model.
10 hikers wore both boots on different hikes and rated comfort on a scale from 0–10.
The table below shows the comfort ratings for each hiker using both boots:
Part 1: What type of test is appropriate for this scenario?

• 2-sample t-test

• Paired sample t-test

• 1-sample t-test

• 2-proportion z-test

Part 2: What are the correct null and alternative hypotheses?

• H0:μd=0,H1:μd≠0

• H0:μ1=μ2,H1:μ10,H1:μd=0

• H0:μd=0,H1:μd<0

Part 3: What are the mean and standard deviation of the differences?

• dˉ=2.0, sd=0.65

• dˉ=1.8, sd=0.789

• dˉ=1.5, sd=0.91

• dˉ=1.2, sd=0.63

Part 4: What is the value of the test statistic?

• 5.87

• 6.02

• 7.21

• 3.45

Part 5: What is the P-value for this test?

• 0.00001

• 0.025

• 0.052

• 0.0031

Part 6: What is the correct decision at α = 0.05?

• Fail to reject H0

• Reject H0

• Inconclusive

• Cannot determine

Tags

CCSS.7.SP.A.2

Part 7: What is the correct conclusion based on this test?

• There is no significant difference in comfort.

• There is strong evidence that the new boots provide better comfort.

• There is strong evidence that old boots are more comfortable.

• There is weak evidence of a difference.

Part 8: What is the 95% confidence interval for the mean difference in comfort rating?

• (1.236, 2.364)

• (1.12, 2.88)

• (0.92, 2.15)

• (0.68, 2.97)

Tags

CCSS.HSS.IC.B.4