Question

a manufacturer fills soda bottles. periodically the company tests to see if there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. a random sample of 14 bottles of regular cola has a mean of 501.3 ml of soda with a standard deviation of 3.4 ml. a random sample of 18 bottles of diet cola has a mean of 497.7 ml of soda with a standard deviation of 3.6 ml. test the claim that there is a difference between the mean fill levels for the two types of soda using a 0.10 level of significance. assume that both populations are approximately normal and that the population variances are not equal since different machines are used to fill bottles of regular cola and diet cola. let bottles of regular cola be population 1 and let bottles of diet cola be population 2. step 3 of 3: draw a conclusion and interpret the decision. answer we fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.10 level of significance to say there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. we reject the null hypothesis and conclude that there is sufficient evidence at a 0.10 level of significance to say that there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. we reject the null hypothesis and conclude that there is insufficient evidence at a 0.10 level of significance to say that there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.10 level of significance to say that there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola.

Explanation:

Step1: Recall hypothesis - testing decision rule

If we reject the null hypothesis, we have sufficient evidence to support the claim of a difference. If we fail - to - reject the null hypothesis, we have insufficient evidence to support the claim of a difference.

Step2: Interpret the decision

In hypothesis testing, when we reject the null hypothesis ($H_0:\mu_1=\mu_2$) at a given significance level (here $\alpha = 0.10$), it means there is sufficient evidence to say that there is a difference between the population means.

Answer:

We reject the null hypothesis and conclude that there is sufficient evidence at a 0.10 level of significance to say that there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola.