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.
Answer: the null and alterative hypotheses were tested on if or if not on average a bag of potato chips contains 130 calories. The conclusion is that on average a bag of potato chips contains 130 calories on 95% significant level.
Ho: µ = 130
HA: µ \(\neq\) 130
As stated, the sample observations are independent, sample size is bigger than 30, and the population distribution skew level is acceptable to be considered as normal. The three conditions for sampling distribution of mean is nearly normal and the estimate of SE sufficient accurate are met. The p value is greater than 0.05, the null hypothesis was not rejected..
(se <- 17/sqrt(35))## [1] 2.873524(z <- round((134 - 130)/se, 2))## [1] 1.39# z-score of 1.39 indicates the lower unshaded area found 0.9177
(area <- 0.5 + 0.4177)## [1] 0.9177(p_value <- (1 - area)*2)## [1] 0.1646p_value < 0.05## [1] FALSEDiez DM, Barr CD, C¸ etinkaya-Rundel M. 2015. openintro: OpenIntro data sets and supplement functions. github.com/OpenIntroOrg/openintro-r-package.