Real Fruit Juice (Raw Data, Software Required): A 32 ounce can of a popular fruit drink claims to contain 20% real fruit juice. Since this is a 32 ounce can, they are actually claiming that the can contains 6.4 ounces of real fruit juice. The consumer protection agency samples 30 such cans of this fruit drink. The amount of real fruit juice in each can is given in the table below. Test the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces. Test this claim at the 0.10 significance level.
DATA ( n = 30 )
Real Juice
ounces |
6.35 |
6.58 |
6.59 |
6.42 |
6.30 |
6.05 |
6.32 |
6.09 |
6.14 |
6.08 |
6.54 |
6.05 |
6.54 |
6.04 |
6.68 |
6.37 |
6.57 |
6.49 |
6.00 |
6.15 |
6.26 |
6.30 |
5.83 |
6.62 |
5.75 |
6.74 |
6.49 |
6.79 |
6.35 |
6.29 |
(a) What type of test is this? This is a left-tailed test. This is a right-tailed test. This is a two-tailed test.
(b) What is the test statistic? Round your answer to 2 decimal places.
(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
(d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0
(e) Choose the appropriate concluding statement.
a. There is enough data to justify rejection of the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.
b. There is not enough data to justify rejection of the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.
c. We have proven that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.
d. We have proven that the mean amount of real fruit juice in all 32 ounce cans is not 6.4 ounces.
let us consider the null and alternative hypothesis is
H0:u = 6.4
Ha:u 6.4
a ) This is a two-tailed test.
using minitab>stat>basic stat>one sample t
we have
One-Sample T: ounces
Test of μ = 6.4 vs ≠ 6.4
Variable N Mean StDev SE Mean 95% CI T P
ounces 30 6.3257 0.2663 0.0486 (6.2262, 6.4251) -1.53
0.137
(b) the test statistic is -1.53
(c) the P-value of the test statistic is 0.1366
(d) since p value is greater than 0.05 fail to reject H0
e ) a. There is enough data to justify rejection of the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.
Get Answers For Free
Most questions answered within 1 hours.