Question

Real Fruit Juice: 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 56 such cans of this fruit drink. Of these, the mean volume of fruit juice is 6.36 with standard deviation of 0.21. 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 0.05 significance level.

(a) What type of test is this?

This is a two-tailed test.

This is a left-tailed test.    

This is a right-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
t-<sub>x= 2

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value = 3

(d) What is the conclusion regarding the null hypothesis?</sub>

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

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.

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.

We have proven that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.

We have proven that the mean amount of real fruit juice in all 32 ounce cans is not 6.4 ounces

Answer 1

Solution:

Test the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.

i.e. = 6.4

So hypothesis are

H0: = 6.4 ....null hypothesis

H1:    6.4 ....alternative hypothesis

Given ,

n = 56 ....sample size

= 6.36 ...sample mean

s = 0.21 ....Sample standard deviation

= 0.05    .... level of significance

a) This is a two-tailed test.

b) The test statistic t is

t =  

= (6.36 - 6.4)/(0.21/56)

= -1.43

c) Degrees of freedom = n -1 = 56 - 1 = 55

t = -1.43

Two tailed test

Using this information

p value = 0.1584

d) Since p value is greater than = 0.05

fail to reject H₀    

e)concluding statement.

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.