10. Hypothesis Testing for Two Samples

Two Means - Matched Pairs (Dependent Samples)

10. Hypothesis Testing for Two Samples

Two Means - Matched Pairs (Dependent Samples)

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Multiple Choice

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.

Difference for each client: $A=4,B=4,C=3,D=-1,E=0,F=2$ ; The Mean Difference = $2$ ; and Standard Deviation = $1.91$

Difference for each client: $A=4,B=4,C=3,D=-1,E=0,F=2$ ; The Mean Difference = $2.5$ ; and Standard Deviation = $1.91$

Difference for each client: $A=4,B=4,C=3,D=-1,E=0,F=2$ ; The Mean Difference = $2.5$ ; and Standard Deviation = $2.10$

Difference for each client: $A=4,B=4,C=3,D=-1,E=0,F=2$ ; The Mean Difference = $2$ ; and Standard Deviation = $2.10$

Verified step by step guidance

Step 1: Calculate the difference (After - Before) for each client. Use the values from the table: Client A: 26 - 22 = 4, Client B: 23 - 19 = 4, Client C: 27 - 24 = 3, Client D: 20 - 21 = -1, Client E: 18 - 18 = 0, Client F: 25 - 23 = 2.

Step 2: Compute the mean difference. Add all the differences calculated in Step 1 (4 + 4 + 3 - 1 + 0 + 2) and divide by the number of clients (6). The formula for mean difference is:

\frac{\sum d}{n}

, where d represents the differences and n is the number of clients.

Step 3: Calculate the squared deviations from the mean for each difference. For each client, subtract the mean difference from their individual difference, then square the result. The formula is:

(^{d - mean) 2}

Step 4: Compute the variance. Add all the squared deviations calculated in Step 3 and divide by the number of clients minus 1 (n - 1). The formula for variance is:

\frac{\sum (^{d - mean) 2}}{n - 1}

Step 5: Calculate the standard deviation. Take the square root of the variance calculated in Step 4. The formula for standard deviation is:

\sqrt{\frac{\sum (^{d - mean) 2}}{n - 1}}

8:33m

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