Homework SourseA study of the sodium content in a 6fluid ounce serving of a
A study of the sodium content in a 6-fluid ounce serving of a soft drink is conducted. These data are obtained on various types of ginger ales and cola drinks:
It is thought that the variability in the sodium content in ginger ales is smalller that that of colas.
a.) What are they hypotheses?
b.) Calculate the test statistic:
c.)What is the critical value of the test?
d.) What is your decision about the null hypothesis?
| Ginger Ale | Cola |
| n1 = 10 | n2 = 10 |
![\"\\bar{x}](\"//d2vlcm61l7u1fs.cloudfront.net/media/f44/f4468853-487b-442f-aaf9-1e09452aeb87/5ac5061d86f31.gif\"/) | ![\"\\bar{x}](\"//d2vlcm61l7u1fs.cloudfront.net/media/add/add61772-f6a2-437a-938a-1fc2ccd110d1/5ac5061e63c42.gif\"/) |
![\"s_{1}^{2}\"](\"//d2vlcm61l7u1fs.cloudfront.net/media/fa0/fa0dfd92-4786-423b-8f7a-93f94be0a078/5ac5061f3a8f3.gif\"/) = 10.89 | ![\"s_{2}^{2}\"](\"//d2vlcm61l7u1fs.cloudfront.net/media/7f2/7f209012-3495-42d7-9d59-6da3f13e755d/5ac5062024e2c.gif\"/) = 11.90 |
Solution
A.
Ho: s1^2 / s2^2 >= 1
Ha: s1^2 / s2^2 < 1
B.
As
F = s1^2 / s2^2,
then
F = 0.91513 [ANSWER]
***************
C.
As df1 = n1 - 1 = 9, df2 = n2 - 1 = 9
Then, at 0.05 significance,
Fcrit = 0.314574906 [ANSWER]
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Thus, we fail to reject the null hypothesis. [ANSWER]
We do not have sufficient evidence that the variability in the sodium content in ginger ales is smalller that that of colas.
