Question

based on the random sample, the sample mean and sample standard deviation are computed as 10.11125 and 0.03871, respectively. assume that the population is approximately normal with unknown population standard deviation. can you conclude that the mean volume is greater than 10 ounces? use the 10% level of significance.

Answer 1

At the 10% significance level, we can conclude that the mean volume is more than 10 ounces.

How to solve this

This is how the hypothesis testing is broken down:

The population mean is less than or equal to 10 ounces, which is the null hypothesis.

A different possibility is that the population mean is higher than 10 ounces.

Level of significance: α = 0.1

Test statistic: t = (0.03871 / sqrt(100)) - (10.11125 - 10) = 32.57 Degrees of freedom df is equal to 100 - 1 = 99.

T_critical = 1.660 is the critical value (from the t-distribution table).

We reject the null hypothesis because the test statistic (32.57) is higher than the crucial threshold (1.660). This indicates that there is enough data to draw the conclusion that the average population volume is higher than 10 ounces.