4.23 Nutrition labels

The nutrition label on a bag of potato chips says that a one ounce (28 gram) serving of potato chips has 130 calories and contains ten grams of fat, with three grams of saturated fat. A random sample of 35 bags yielded a sample mean of 134 calories with a standard deviation of 17 calories. Is there evidence that the nutrition label does not provide an accurate measure of calories in the bags of potato chips? We have verified the independence, sample size, and skew conditions are satisfied.

The associated hypotheses are:

1. Ho: u = 130: Average calories in a bag of potato chips is 130 calories
2. Ha: u <> 130: Average calories in a bag of potato chips is not 130 calories

Test Statistic:

In order to evaluate if the observed sample mean is unusual for the hypothesized sampling distribution, we determine how many standard errors away from the null it is, which is also called the test statistic Z.

p-value:

We then use this test statistic to calculate the p-value, the probability of observing data at least as favorable to the alternative hypothesis as our current data set, if the null hypothesis were true.

If the p-value is low (lower than the significance level, 0.05) we say that it would be very unlikely to observe the data if the null hypothes is were true, and hence reject Ho.

If the p-value is high (higher than 0.05) we say that it is likely to observe the data even if the null hypothesis were true, and hence do not reject Ho.

Solution:
Ho = u = 130, Ha = u <> 130, sample mean x = 134, The sample population s = 35, standard deviation n = 17

Z = (134 - 130) / (17 /sqrt(35) ) 
Z

## [1] 1.392019

Calculating the p-value:
p(1.39) = 0.08822 * 2 = 0.1645

Conclusion:
The p-value is larger than 0.05. The data does not provide convincing evidence that the true average calorie content in a bag of potato chips is different than 130 calories. Hence we do no reject the null hypotheses.