Sampling Distributions for Means Question 10

A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses $H_0 : \mu=12$ versus $H_a : \mu \lt 12$ was conducted, where $\mu$ represents the population mean number of ounces of the beverage dispensed per bottle by the machine. The $p$ -value for the test was 0.08. Which of the following is the most appropriate conclusion to draw at the significance level of $\alpha$ = 0.05 ?

Because the

p

-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Because the

p

-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.

Because the

p

-value is greater than the significance level, there is not convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.

Because the

p

-value is less than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Approach

Since the $p$ -value is less than $\alpha$ , we fail to reject the null hypothesis. In other words, there isn't enough convincing evidence against the null hypothesis