Answer to Question #152467 in Statistics and Probability for juls

Question

A super, market has been selling discounted apples in bundles of five at their counters. A random sample of 49 bundles weighs 980 grams on average, with a standard deviation of 65 grams. Test the hypothesis that . = 1000 grams against the alternative hypothesis of > 1000 at 0.07 level of significance

Answer 1

Hypothesis testing for a mean (σ is unknown, and the variable is normally distributed in the population or n > 30 )

So we use t-test with df = n-1 = 49-1 = 48 degree of freedom:

$P(X\ge1000) = P(t_{48} \ge \frac {\mu_X-1000} {\sigma_X}) =\\ P(t_{48} \ge \frac {980 - 1000} {65/ \sqrt{49}}) = P(t_{48} \ge -2.15) = \\ 1-P(t_{48}< -2.15)=\\ 1-0.018 = 0.982>0.07$

Hence, we cannot reject the null hypothesis that the population mean is equal to 1000 at significant level of 0.07.