Question

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.52 liters. a health campaign promotes the consumption of at least 2.0 liters per day. a sample of 10 adults after the campaign shows the following consumption in liters: 1.66 1.40 1.70 1.96 1.74 2.02 1.92 1.84 1.66 1.72 at the 0.100 significance level, can we conclude that water consumption has increased? calculate and interpret the p-value.

Answer 1

The question involves testing if there is a significant increase in water consumption following a health campaign, using a one-sample t-test at a 0.100 significance level. A p-value less than 0.100 would mean a significant increase in consumption.

Step-by-step explanation:

The student is asking whether the average daily water consumption has increased following a health campaign, using a sample of 10 adults and a 0.100 significance level. Based on the provided sample data, one would conduct a one-sample t-test to compare the sample mean to the known population mean before the health campaign. Calculation of the p-value will determine if there is a significant increase in water consumption.

To calculate the p-value, we first need to compute the sample mean (x-bar) and the sample standard deviation (s) of the given water consumption data. These values, along with the sample size (n), are used to determine the t-statistic. The p-value is then obtained by comparing the t-statistic to a t-distribution with n-1 degrees of freedom. A p-value less than the significance level (0.100) would indicate a statistically significant increase in water consumption.

If the p-value is less than the significance level, we can conclude that there is sufficient evidence to suggest that the health campaign has effectively increased water consumption.