Question

Calories in Pancake Syrup A nutritionist claims that the standard deviation of the number of calories in 1 tablespoon of the major brands of pancake syrup is 60. A random sample of major brands of syrup is selected, and the number of calories is shown. At α = 0.10, can the claim be rejected?

Source: Based on information from Netzer, Corinne T., The Complete Book of Food Counts. New York: Dell Publishers, 2011.

Answer 1

To determine whether the claim can be rejected, we need to perform a hypothesis test to compare the sample standard deviation to the claimed standard deviation. If the test statistic is greater than the critical value, we can reject the null hypothesis.

To determine whether the claim can be rejected, we need to perform a hypothesis test. The null hypothesis would be that the standard deviation of the number of calories in 1 tablespoon of pancake syrup is not greater than 60. The alternative hypothesis would be that the standard deviation is greater than 60.

We can then calculate the test statistic using the sample standard deviation and the degrees of freedom. The degrees of freedom can be calculated as the sample size minus 1. We can then compare the test statistic to the critical value from a t-distribution with the appropriate degrees of freedom and significance level α = 0.10.

If the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that the standard deviation is greater than 60. If the test statistic is not greater than the critical value, we fail to reject the null hypothesis and do not have enough evidence to conclude that the standard deviation is greater than 60.