Question

There are hundreds of apples on the trees, so you randomly choose just 45 apples and get a mean weight of 89.05 grams with a standard deviation of 4.43 grams. Assuming that the weight of the apples is normally distributed, what is the standard error of the 90% confidence interval for the mean weight of the apples

Answer 1

The critical value for $\alpha = 0.1$ and $df = n-1 = 44$ degrees of freedom is $t_c = z_{1-\alpha/2; n-1} =1.68023.$

The standard error of the 90% confidence interval for the mean weight of the apples is

$$SE_{\bar{X}}=s/\sqrt{n}=4.43/\sqrt{45}\approx0.66038541$$