a) State the null and the alternative hypothesis.
Null hypothesis (H0): The residents of the kebele have the same mean weight as the city's general population (μ = 130 lbs).
Alternative hypothesis (H1): The residents of the kebele have a significantly different mean weight than the city's general population (μ ≠130 lbs).
b) Give the critical region
We are given a 1% level of significance, and since this is a two-tailed test, we will be looking at 0.5% at each tail.
For a two-tailed test with a 1% level of significance, we use the Z critical values: -2.576 and 2.576.
c) What is your decision?
To make a decision, we need to calculate the test statistic.
Test statistic (Z) = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
Z = (129 - 130) / (41 / sqrt(25))
Z = (-1) / (41 / 5)
Z = (-1) / 8.2
Z ≈ -0.122
Since -0.122 is not in the critical region (-2.576, 2.576), we fail to reject the null hypothesis.
Decision: There is no significant evidence at the 1% level of significance to suggest that the residents of the kebele weigh significantly less or more than the general population of the city.