Answer Happy

1 Mean of normal, variance given [ One sample Z-test] 1. Population N(u, a) with variance ² known. Null hypothesis: Ho: p=po (population mean is a specific given value po) Natural Estimator for μ: X. Input: Level of significance a, 71, 72,..., observed sample. X-Ho Test statistic: Z= Distribution of test statistic if the null hypothesis holds true: N(0, 1) (standard normal). Why? 44140 μ> μο kế ho Alternative H₁ |2|> a/2 Test (critical region): Sketch of CR (under pdf): 2. It is advertised that one cup of ice-cream will have 20 grams. Assume that the distribution of amount of ice-cream in a cup is normal with mean μ, variance o² = 4g. The tester selected 10 cups at random and found that their average weight is 21.5g. To check whether things are going as advertised, test the null hypothesis that the population mean is μ = 20g against the alternative that it is not (ie, μ #20) at 0.01 level of significance. Report the outcome (ie, whether null hypothesis rejected or not rejected.) 3. In the previous question, what is the p-value based on the observed sample? 4. In the question (2) above, what is the test outcome if the alternative was population mean is greater than 20g (ie, μ > 20)?