A personal trainer is studying whether a new stretching routine improves flexibility. She records the forward reach (in cm) of 6 clients before and after a 4-week program. Calculate the difference (after - before) for each client, the mean difference, and standard deviation.
Table of contents
- 1. Introduction to Statistics53m
- 2. Describing Data with Tables and Graphs2h 1m
- 3. Describing Data Numerically1h 48m
- 4. Probability2h 26m
- 5. Binomial Distribution & Discrete Random Variables2h 55m
- 6. Normal Distribution & Continuous Random Variables1h 48m
- 7. Sampling Distributions & Confidence Intervals: Mean2h 8m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 20m
- 9. Hypothesis Testing for One Sample2h 23m
- 10. Hypothesis Testing for Two Samples3h 25m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 30m
- 14. ANOVA1h 4m
10. Hypothesis Testing for Two Samples
Two Means - Matched Pairs (Dependent Samples)
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Construct a 95% confidence interval for the mean difference of the population given the following information. Would you reject or fail to reject the claim that there is no difference in the mean?
dˉ=−0.728
sd=1.34
n=10
A
The 95% confidence interval = (−1.152,−0.304); Fail to reject the claim that there is no difference in the mean.
B
The 95% confidence interval = (−1.686,0.230); Fail to reject the claim that there is no difference in the mean.
C
The 95% confidence interval = (−1.686,0.230); Reject the claim that there is no difference in the mean.
D
The 95% confidence interval = (−1.152,−0.304); Reject the claim that there is no difference in the mean.

1
Step 1: Identify the given information. The sample mean difference (d̄) is -0.728, the standard deviation of the differences (s_d) is 1.34, and the sample size (n) is 10. The confidence level is 95%.
Step 2: Calculate the standard error of the mean difference (SE_d). The formula for the standard error is SE_d = s_d / sqrt(n), where s_d is the standard deviation and n is the sample size.
Step 3: Determine the critical t-value for a 95% confidence level with degrees of freedom (df = n - 1). Use a t-distribution table or statistical software to find the t-value corresponding to a two-tailed test with df = 9.
Step 4: Calculate the margin of error (ME) using the formula ME = t * SE_d, where t is the critical t-value and SE_d is the standard error calculated in Step 2.
Step 5: Construct the confidence interval using the formula: Confidence Interval = d̄ ± ME. Substitute the values of d̄, ME, and calculate the lower and upper bounds of the interval. Finally, compare the interval to the claim (0 difference) to decide whether to reject or fail to reject the null hypothesis.
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