Question

Mathematical Statistics 2018/2019, Homework 9 Name and Surname Student's number In the problems below, please use the following: as k - the sum of digits in youir student's number; as m - the sum of the two largest digits in your student's number; and as n - the smallest digit in your student's number plus 1. For example, if an index number is 609999: k-42, m-18, n 1 Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in decimal notation, rounded to four digits 9. A group of k students were surveyed regarding the amount of money they earn in temporary jobs during their summer break. Assuming that the amount earned (in hundreds of euro) follows a normal distribution with mean μ and variance equal to m2, where μ > 0 is an unknown parameter we want to verify the null hypothesis that μ-m, against the alternative that it is less. What is the critical region of a (2n)% significance level test for these hypotheses? What is the value of the appropriate test statistic, if the sample average was equal to m - 2n? What is the p-value of this result? What is the decision? ANSWE Critical region Value of Reject null? (YES/NO) p-value of test statistic: test statistic: of the test: Solution

K=42, m=18 , n=4

Answer 1

k =42, m = 18, n=4

Here we have to test that

0:11 = 18

1.1 < 18

$\bar{x}=m-2*n=18 - 2*4=10$

σ2-m2-182-324

$\sigma =18,\mu _0=18$, k =sample size = 42

Test statistic:

$z_0=\frac{\bar{x}-\mu _0}{\sigma /\sqrt{k}}$

10 18 1 to = 18/v 42

Z0 = -2.88         (Round to 2 decimal)

Test statistic = z0 = -2.88

P value = P(Z < Z0)

             = P(Z < -2.88)

             = 0.0020                    (From statistical table of negative z values)

P value = 0.0020

Here alpha = level of significance = (2n)% = (2*4)% = 8% = 0.08

Here P value < alpha

So we reject null hypothesis H0