A soft-drink manufacturer claims that its 12-ounce cans do not contain, on avera

Question

A soft-drink manufacturer claims that its 12-ounce cans do not contain, on average, more than 30 calories. A random sample of 70 cans of this soft drink, which were checked for calories, contained a mean of 32 calories with a standard deviation of 3 calories. Does the sample information support the alternative hypothesis that the manufacturer's claim is false? Use a significance level of 5%. Find the range for the p-value for this test. What will your conclusion be using this p-value and =0.05? Use the t distribution table to find a range for the p-value.

Explanation / Answer

We want to test hypothesis

H0: mu=30 against H1: mu > 30

From the information

n=70 xbar=32 and s.d= 3

since population variance is unknown we use one sample t-test

under H0 the test statistic is

t =( xbar-mu)/(s.d/sqrt(n))~tn-1

t = ( 32-30)/(3/sqrt(70))

= 5.5777

To obtained p-value for t=5.577 7 and d.f= 69

p-value= 0.00001

level of significance=0.05

since p-value is very small as compared to level of significance.

Hence there is strong evidences to reject the null hypothesis at 5% level of sigmificance.

Conclusion : Manufactures Claims that its 12 -ounce can do not contain on avarage more than 30 calories is false.

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