Question

The manager of a chip bag factory wants to test whether the average bag weight is stable at 32 g. He weighs 100 bags chosen at random and finds an average of 31.8 g with a standard deviation of 0.8 g.

Has the average potato chip weight changed significantly?

Answer 1

To determine if the average potato chip weight has changed significantly, a hypothesis test can be performed using a t-test to compare the sample mean to the population mean, taking into account the sample size and standard deviation.

Step-by-step explanation:

To determine if the average potato chip weight has changed significantly, we can perform a hypothesis test. The null hypothesis (H0) is that the average bag weight is stable at 32 g, and the alternative hypothesis (Ha) is that the average bag weight has changed.

We can use a t-test to compare the sample mean (31.8 g) to the population mean (32 g), taking into account the sample size (100) and the standard deviation (0.8 g). Based on the test statistic and the p-value, we can determine if the difference in average weights is statistically significant.

After conducting the t-test, if the p-value is less than the significance level (commonly chosen as 0.05), we reject the null hypothesis and conclude that the average potato chip weight has changed significantly. Otherwise, if the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant change in the average weight of the chips.