Question

I need to do these questions by only using Excel but want to make sure all my functions are correct. I would appreciate a lot if you could help me with this question. Thanks!

3. The aim of this exercise is to perform a hypothesis test involving a population mean where the population standard deviation is known. You may follow Pg 131-138 of your textbook to complete the calculations involved in this exercise. Experience has shown that the scores obtained in a particular test are Normally distributed with mean score 70 and standard deviation 6. When the test is taken by a random sample of 36 students, the mean score is 68.5. Is there sufficient evidence, at the 3% significance level, that these students have not performed as well as expected? (a) Showing clearly how you obtain your answer, calculate the P-value for the test. [3 marks] (b) What conclusion can you draw at the 3% significance level? [1 mark]

Answer 1

a)

A F14 А 1 Given Population Mean = mu = 3 Sample size n = 4 Sample Mean = Xbar = 5 Population SD = (0) = LOS = a = fx = (B4-B2)/(B5/SQRT(B3)) C D E F G Z- test for single mean Step 1: 36 HO: The students have performed as well as expected 68.5 Ho u = 70 i.e. 0.03 H1: The students have not performed as well as expected i.e. H: u < 70 Step 2: b) Decision: Reject He if test statistic (Z.) value < critical value (Za) alpha = Z crit = (Za) = -1.8808 ENORM.S.INV(F10) Step 3: Test statistic -1.5 =(B4-B2)/(B5/SQRT(B3)) Step 4: P-value = 0.0668 ENORM.S.DIST(F14,TRUE) Step 5: Here Zo value is greater (or) p-value > than critical value Za so we alpha ( = 0.03 so we accept Ho accept Ho Decision: Thus, we conclude that the students have performed as well as expected

or

For only P-value

for ENORM.DIST(B4,B2,D3, TRUE) TD E F G D5 A 1 Given 2 Population Mean = mu = 3 Sample size n= 4 Sample Mean = Xbar = Population SD = (0) = LOS = a = SE = 1 =B5/SQRT(B3) 5 P-value = 0.0668 ENORM.DIST(B4,B2,D3,TRUE) 0.03

b) Thus we conclude that The students have performed as well as expected