Question

A proposed null hypothesis states that there is no difference in the population mean heights of males of two neighboring towns. The sample mean difference is found to be 10 cm, and the standard deviation of the difference of the sample means is 6 cm. Which statement is true? The null hypothesis must be rejected if we choose the 68% confidence level. The null hypothesis must be rejected if we choose the 95% confidence level. The null hypothesis must be rejected if we choose the 99.7% confidence level. The null hypothesis must be rejected if we choose the 100% confidence level. NextReset

Answer 1

From the problem, we are given
x1 - x 2 = 10 cm
s of (x1 - x2)i = 6 cm
The null hypothesis is that there is no significant difference between the height of males of the two neighborhoods.

For the null hypothesis to be rejected, this condition must be met
u1 - u2 ≠ 0

For a normal distribution
u = x + z s / √n
where z depends on the confidence interval (CI)
If
CI = 67%, z = 0.16
CI = 95%, z = 0.025
CI = 99.7%, z = 0.0015
CI = 100%, z = 0
So,
u1 - u2 = x1 + z s1 √n - (x2 - z s2 /√n )
Substituting the given values and trying out the different values of z for different confidence intervals, the CI that would meet the required condition is
CI = 95%
So, the answer is
The null hypothesis must be rejected if we choose the 95% confidence level.