A marketing research firm wishes to compare the prices charged by two supermarke
ID: 3151219 • Letter: A
Question
A marketing research firm wishes to compare the prices charged by two supermarket chainsMillers and Alberts. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chains stores. The stores for each chain are randomly selected, and all purchases are made during a single week. It is found that the mean and the standard deviation of the shopping expenses at the 10 Millers stores are formula x1=123.75 and s1= 1.44. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Alberts stores are formula x2=117.15 and s2= 1.66. Assuming normality, test to see if the corresponding population standard deviations differ by setting ? equal to .05. Is it reasonable to use the equal variances procedure to compare population means? (a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Test statistic (b) Calculate the critical value. (Round your answer to 2 decimal places.) Critical value
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: sigma1^2 / sigma2^2 = 1
Ha: sigma1^2 / sigma2^2 =/ 1
As we can see, this is a two tailed test.
Getting the test statistic, as
s1 = 1.44
s2 = 1.66
Thus, F = s1^2/s2^2 = 0.752503992 [ANSWER]
********************
b)
Thus, getting the critical F, as alpha = 0.05 ,
alpha/2 = 0.025
df1 = n1 - 1 = 9
df2 = n2 - 1 = 9
F (crit) = 0.248385855 and 4.025994158 [ANSWER]
*******************
Hi! I assumed this is a two tailed test (hence two critical value). If you use just 1 tail, then
Fcrit = 3.178893104 [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.