Question

A potato chip company claims that their chips have 130 calories per serving. We think this claim is too low, so we buy 40 bags of chips and test the calories per stated serving size.  Our sample yields a mean of 132 calories per serving, with a standard deviation of 6 calories. Is the manufacturer's claim too low? \

Use alpha = 0.05.

Answer 1

Right Tailed t test, Single Mean

Given: = 130 calories, = 132 calories, s = 6 calories, n = 40, = 0.05

The Hypothesis:

H0: = 130: The mean calories per serving of potato chips is equal to 130 calories. (Claim)

Ha: > 130: The mean calories per serving of potato chips is greater than 130 calories.

This is a Right tailed test

The Test Statistic: Since the population standard deviation is unknown, we use the students t test .

The test statistic is given by the equation:

t observed = 2.11

The p Value: The p value (Right tailed) for t = 2.11, for degrees of freedom (df) = n-1 = 39, is; p value = 0.0207

The Critical Value: The critical value (Right Tail) at = 0.05, for df = 39, tcritical= +1.685

The Decision Rule:  

The Critical Value Method: If tobserved is > tcritical.

The p-value Method: If P value is < , Then Reject H0.

The Decision:

The Critical Value Method: Since tobserved (2.11) is > t critical (1.685), we Reject H0.

The p-value Method: Since P value (0.0207) is < (0.05) , We Reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to warrant rejection of the claim that the mean calories per serving of potato chips is equal to 130 calories.