In Exercises 7–10, (d) explain how you should interpret a deci...

Question

In Exercises 7–10, (d) explain how you should interpret a decision that rejects the null hypothesis.

An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A juice company claims the average vitamin C content in its product is less than 60 mg per serving. After performing a hypothesis test, you reject the Noel hypothesis. What is the correct interpretation? Awesome. So it appears for this particular prompt we're asked to take all the information that is provided to us by the prom itself, meaning the context, and we're asked to determine what is the correct interpretation for this particular prom. So we're given a claim and we're we determine based on the claim that's made, that when we perform a hypothesis test, we reject the null hypothesis. And based on those two pieces of information, we're asked to make a correct interpretation, and that is our final answer that we're ultimately trying to solve for. So with that in mind, our first step that we need to take in order to solve this problem is we need to state the null hypothesis, and as we should recall, we can denote the null hypothesis as H subscript zero, and we can say for the null hypothesis. That when let's say that mu, let's denotemu as the mean vitamin C content per serving. So once again, mu denotes the mean vitamin C content per serving. So we can say for the null hypothesis, mu is equal to 60, because once again we're told that the average Vitamin C content in its product is less than 60 mg per serving. So, and once again, the average and mean, both words are used interchangeably, so the average is the same as the mean vice versa. So we're going to use mu to denote the average. So, moving right along here, our second step is we need to state the alternative hypothesis, which will denote as H subscript A, and our alternative hypothesis HA, we can say that mu is less than 60. And for our third step, we need to note that we are rejecting the null hypothesis, so I'll put H0 with an X next to it. So we're rejecting the null hypothesis, which means that the data supports mu is less than 60, so I'll put a green check mark next to mu is less than 60. So once again, since we are rejecting the null hypothesis, this means as a result, the data supports the claim new is less than 60. So that means for our 4th and final step, As a result, the correct interpretation is that there is statistical evidence to support the claim that the mean vitamin C content is indeed less than 60 mg. So that means our final answer, without a doubt has to be the following. There is statistical evidence that the mean vitamin C content is less than 60 mg, and that's it. That is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

In Exercises 7–10, (d) explain how you should interpret a decision that rejects the null hypothesis.

An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

Key Concepts

Null Hypothesis

Alternative Hypothesis

Statistical Significance

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