Math 1340 Take Home Assignment 12 Name: 1. Two independent random samples of peo
ID: 3219743 • Letter: M
Question
Math 1340 Take Home Assignment 12 Name: 1. Two independent random samples of people were selected. The respondents rated two colas (A and B) on a scale of 1 to 10. Here is a table summarizing the results Cola B Cola A 7.22 7.92 Sample Mean Sample Size Sample Standard 2.7 1.4 Deviation Test the claim that Cola A is preferred over Cola B at the 0.05 significance A: State the Claim and Hypotheses B: Find the Test Statistic c: Find the critical value(s) for this test D: Would we reject or fail to reject the null hypothesis? E: State the proper conclusion.Explanation / Answer
x1 = 7.92 , x2 = 7.22 , n1 = 38 , n2 = 45 , s1 = 2.7 , s2 = 1.4
1) Hypothesis:
H0 : mu1 - mu2 = 0
Ha : mu1 - mu2 > 0
2) Test statistic;
SE = sqrt [(s12/n1) + (s22/n2)]
SE = sqrt[(2.72/38) + (1.42/45]
= 0.48
t = [ (x1 - x2) - d ] / SE
= [ (7.92 - 7.22) - 0 ] / 0.48
= 1.46
c) Critical value
The critical value of t for 0.05 with df =81 = 1.6639
d) we fail to reject the null hypothesis because 1.46 < 1.6639
e) We conclude that there is not sufficeient evidence to support that cola A is preferred over cola B