Question

we are interested in seeing if there is a statistically difference between the number of calories eaten daily, on average, by people in America and people in England. We are given the following information America England Sample mean 3770 3440 Population Variance 65025 90000 n 42 30 Find the 98% confidence interval for the difference in the calories eaten in the two countries.

Answer 1

Explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

z = (x1 - x2) ± √(s1²/n1 + s2²/n2)

Where

x1 = sample mean of group 1(America)

x2 = sample mean of group 2(England)

s1 = sample standard deviation for data 1

s2 = sample standard deviation for data 2

For a 98% confidence interval, the z score is 2.326

From the information given,

Standard deviation = √variance

x1 = 3770

s1 = √65025 = 255

n1 = 42

x2 = 3440

s2 = √90000 = 300

n2 = 30

x1 - x2 = 3770 - 3440 = 330

√(s²/n1 + s2²/n2) = √(225²/42 + 300²/30) = √1205.357 + 3000)

= 64.9

The upper boundary for the confidence interval is

330 + 64.9 = 394.9

The lower boundary for the confidence interval is

330 - 64.9 = 265.1