Please use the following information to answer 11a-11e:

Montarelloand Martens (2005) found that fifth-grade students completed more matematicsproblems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics acheivement test that produces a normal distribution of scores with a mean of= 100 and a standard deviation of= 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions, and gives the modified test to a sample ofn= 36 students. If the average test score for the sample isx= 104, is this result sufficient to conclude that inserting the easy questions improves performance?Use a one-tailed test with= .01.

11a. Which of the following correctly represents the null and alternative hypothesis for the mentioned sample ofn=36 (MUST SHOW WORK FOR THIS PROBLEM)?

a) Ho:= 100

H_1: 100

b) Ho:> 100 H_1: 100

c) Ho: 100 H_1:> 100

d) Ho: 100 H_1:< 100

11b.Which of the followingrepresents the critical region for this mentioned sample(MUST SHOW WORK FOR THIS PROBLEM)?

a) z=2.33

b) z=2.33

c) z=2.58

d) z=2.58

11c.Compute the test statistic(z-observed)for the mentioned sample(MUST SHOW WORK FOR THIS PROBLEM).

Note:Must show calculations for standard error alongside the calculations for the test statistic.

11d.Based on the calculated test statistic,would you reject the null hypothesis established in question11a (MUST SHOW WORK FOR THIS PROBLEM)?

a) yes

b) no

11e.Based on the previouslyconducted steps,we can conclude(MUST SHOW WORK FOR THIS PROBLEM):

a) Performance was significantly improved whenadding easy questions to a standardized mathematicsachievementtest.

b) Performance was not significantly improved when adding easy questions to a standardized mathematics achievementtest.

c) Performance was unaffected/remained stablewhen adding easy questions to a standardized mathematics achievementtest.

d) Performance was significantly differentwhenadding easy questions to a standardized mathematicsachievementtest.