Question

Using the data presented by Hand and colleagues† and discussed in previous chapters, we would like to estimate the average difference between the heights of adult British men and adult British women. The 200 men in the sample had a mean height of 68. 2 inches, with a standard deviation of 2. 7 inches. The 200 women had a mean height of 63. 1 inches, with a standard deviation of 2. 5 inches. Assuming these were independent samples, compute an approximate 95% confidence interval for the mean difference in heights (in inches) between British males and females. (Round your answers to two decimal places. )

Answer 1

• Answer: (4.59, 5.61 ) INCHES

The approximate Ninety-Five (95%) Confidence Interval for the Mean Difference in heights between BRITISH MALES and FEMALES:

(4.59, 5.61 ) INCHES

• Step-by-step explanation: ±, ≠, √a, x, s 2

• MAKE A PLAN:

We will use the FORMULA for the CONFIDENCE INTERVAL of the DIFFERENCES between TWO INDEPENDENT MEANS, Which is given by:

• FORMULA:

CI = ( x1 - x2 ) ± z * √s^2 1/n1 + s^2 2/n2

• SOLVE THE PROBLEM:

(1) - Calculate the difference between the means:

x1 - x2 = 68.2 - 63.1 = 5.1

(2) - Calculate the Standard Error:

√s^2 1/n1 + s^2 2/n2 = √2.7^2/200 + 2.5^2/200

= √7.29/200 + √6.25/200

= √0.00677

= √0.2602

(3) - Find the Critical Value for a Ninety-FIVE (95%) Confidence Interval, (Using a standard regular/normal distribution table).

z = 1.96

(4) - Calculate the Confidence Interval:

CI = 5.1 ± 1.96 * 0.2602 = (5.1 - 1.96 * 0.2602, 5.1 + 1.96 * 0.2602)

= (4.5908, 5.6092)

• DRAW THE CONCLUSION:

The approximate Ninety-Five (95%) Confidence Interval for the Mean Difference in heights between BRITISH MALES and FEMALES:

(4.59, 5.61 ) INCHES

I hope this helps you!