Question

Problems 9-12: A bottle of Sunny Day orange juice is supposed to contain 64 ounces of juice. A random sample of 25 bottles of orange juice had a mean of 63.8 oz. with a standard deviation of 0.35 oz. Use a 0.05 significance level to test the claim that the mean amount of juice in all bottles is different from 64 ounces. State the appropriate null and alternative hypotheses. B 1 A 9 A ve G a + E = TT 12pt = B 1 x x Paragraph = - HO: mu=64

Answer 1

Solution:

Given

n = 25 sample size

$\mu =\mu o= 64$

Xbar = 63.8 sample mean

S = 0.35. sample standard deviations

$\alpha = 0.05$. Level of significance

To test

Ho:u=64

Vs

$Ha: \mu \neq 64$

Test Statistics

t= Xbar – μο S/ n

$t = \frac{63.8 - 64}{0.35/ \sqrt 25}$

$t = \frac{63.8 - 64}{0.35/ 5}$

$t = \frac{- 0.2}{0.07}$

t = - 2.85714

$t \alpha/2,n-1$.

t 0.025,24 = 2.064. From t table

t critical value = 2.064

Decision

| t | >= t critical value that is

$2.8571 \geq 2.064$

Reject Ho

Conclusion : The mean amount of juice in all bottle different from 64 ounces