Discarded Plastic Data Set 42 “Garbage Weight” includes weight...

Question

Discarded Plastic Data Set 42 “Garbage Weight” includes weights (pounds) of discarded plastic from 62 different households. Those 62 weights have a mean of 1.911 pounds and a standard deviation of 1.065 pounds. We want to use a 0.05 level of significance to test the claim that this sample is from a population with a mean less than 2.000 pounds. Identify the null hypothesis and alternative hypothesis.

Accepted Answer

Hello there. Today we're gonna 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 nutritionist is studying the average daily sugar intake in units of grams among teenagers. From a sample of 40 teenagers, the mean intake is found to be 68 g with a standard deviation of 9 g. The nutritionist wants to test at the 0.05 significance level. The claim that the population mean is not equal to 70 g. What are the correct null and alternative hypotheses? Awesome. So it appears for this particular problem, we're ultimately trying to solve for two separate answers. We're ultimately trying to find the correct values for the null and alternative hypotheses based on all the information that is provided to us by the prom itself. And with that said, now that we know that we're trying to solve for the null and alternative hypothesis values, let's read off our multiple choice answers to see what our final answer pair might be, and they all state that curly bracket of H0, which represents our null hypothesis, and H subscript 1, which which represents our alternative hypothesis. Have some value a mu is either equal to or cannot be equal to or is greater than or less than. So let's read them off to see what our final answer pair might be, noting that I'll read the null hypothesis value from you first and then the alternative hypothesis value for you. So A is mu equals 70, and mu cannot equal 70. B is mu cannot equal 70, and mu is equal to 70. C is mu is greater than 70 and mu is less than 70, and finally D ismu is less than 70 and me is greater than 70. Awesome. So first off, let us note that we are told that the mean sugar intake from a sample of 40 teenagers is 68 g. The standard deviation, which we can denote this as sigma, the standard deviation sigma is equal to 9 g, fantastic. And the nutritionist, as we should note and recall, wants to test the claim that the population mean is not equal to 70 g, and we're also told that the significance level, which will denote as alpha, is equal to 0.05. Fantastic. So what exactly are we testing? So we're ultimately trying to test a claim about the population mean, which we're going to denote the population mean as mu, and we need to note from the prom that the nutritionist believes that the average might not be 70 g, so we are checking to see if the population mean differs from 70. So how do we form the hypothesis values that we're trying to solve for? So for any hypothesis test, as we should recall, the null hypothesis, which once again is H0, always contains the statement of no difference or equality. And the alternative hypothesis, which is H1. Contains the claim being tested, so what the researchers suspects or wants to prove, as we should recall. Therefore, without a doubt, our first major step to solve for this particular problem. we need to note and recall that the null hypothesis states that the population mean is equal to 70 g, so that would mean that for H 0, mu, once again the population means that mu will be equal to 70. And our second step is we need to note and recall that the alternative hypothesis states that the population mean is not equal to 70 g. So that will mean that H1 states that mu cannot equal 70, and that's it. We've officially solved for this particular problem. Hooray, we did it. So looking at our multiple choice answers, and before we look at our multiple choice answers, we should pause and note that. This is a two-tailed test for population mean. So in the future, you should be able to recognize that a problem with similar circumstances will be a two-tail test for the population mean. So with that said, looking at our multiple choice answers, the correct answer has to be multiple choice answer letter A, which once again states that curly brackets of H 0, mu is equal to 70, and H1mu cannot equal 70. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Null Hypothesis

Alternative Hypothesis

Level of Significance

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