Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to perform mean hypothesis testing on a politician's claim of survey results. Here's our problem statement: Assume that adults were randomly selected for a poll. They were asked if they favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos. Of those polled, 483 were in favor, 395 were opposed, and 120 were not sure. A politician claims that people don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Exclude the 120 subjects who said that they were unsure, and use a 1% significance level to test the claim that the proportion of subjects who respond in favor is equal to 50%. What does the result suggest about the politician's claim?
OK, that was a mouthful. Let's get into this. So the first part of our problem asks us to identify the null and alternative hypotheses. The null hypothesis is always a statement of equality, so we're not going to select Answer option C. And then among the three answer options that remain, we can select the correct one by choosing the correct alternative hypothesis.
The alternative hypothesis typically reflects the claim unless the claim has some sort of semblance of equality to it, in which case we'll take the compliment. Here the claim --- we look at the problem statement --- it says we're testing the claim that the proportion of subjects who respond in favor is equal to 50%. So the proportion is equal to 50% is the claim. But that is the null hypothesis, because equality by definition belongs to the null hypothesis. So we have to take the compliment of that. The compliment of being equal to is being not equal to. So we want Answer option A. Nice work!
Alright, the next part of this problem asks us to identify the test statistic. To do that, we're going to have to run a hypothesis test. And the easiest way to do that, for me anyway, is to go into StatCrunch. So I open up StatCrunch, and I'm going to pop this pop out button here so that the window pops out of the window with the problem statement. And now I can move this around. I can resize the window, and I can do all sorts of wonderful little things with this.
OK, so to do our hypothesis test, we're going to go to Stat --> Proportion Stats (because we're dealing with proportions) --> One Sample (because we have only one sample) --> With Summary (because we don't have actual data, just summary stats). Number of successes --- well, what is the success? We're testing the claim that the proportion of subjects who respond in favor is equal to 50%, so responding in favor is going to be our definition of success. How many were in favor? Well, here it says 483 were in favor. So I put that up here.
Number of observations --- this is the total. So I'm going to pull out my --- hey, where did my calculator go? Guess I'll have to --- let me look for my calculator. Oh, there it is. It magically appeared. OK, so here's the calculator. We're going to take the total 483 we're going to add it to the 395 that were opposed, and we don't have to include the 120 because it said to exclude the 120 who said they were unsure. So just those two together. That gives me my total, which doesn't look right. 483 plus 395 is 1273? Uh, I don't think so. Let's try this again. 483 plus 395 is 878. That looks better. I don't know what happened with that. I'll have to check this out.
OK! So that's all we need there. And I'm running a hypothesis test, and these fields match. We selected over here for our null and alternative hypothesis. So I'm all set to go. And here in the table, second to last number in that table as always, is my test statistic. And I'm asked to round to two decimal places. So that is what I'm going to do. Excellent!
Now the next part asks for the P-value. The P-value as always is next to the test statistic, so the last value there in my results window. Fantastic!
"Identify the correct conclusion." Well, our significance level is 1%. The P-value we have is three tenths of a percent. So the P-value is less than the significance level. That means we're inside the region of rejection, and that means we're going to reject the null hypothesis. Every time you reject the null hypothesis, there is always sufficient evidence. So this is the answer option we want. Well done!
And now the last part of this problem asks, "What does the result suggest about the politician's claim?" Well, look here. We rejected the null hypothesis. What's the null hypothesis? The null hypothesis says that the proportion is equal to 50%. Well, we're rejecting that, meaning we're saying this is not true. It's something other than 50%. But the politician --- what did the politician claim? The politician claimed that responses to such questions are random responses equivalent to a coin toss. A coin toss is 50/50 heads or tails. So the politician is claiming that the proportion is 50%, but our hypothesis test resulted in a rejection of that claim. And so therefore we're saying the politician doesn't know diddly squat, which for most politicians is actually pretty spot on.
So let's see here. What are our answer options? "The results suggest the politician is doing his best?" Eh, I don't think so! "The results suggest the politician is correct." I don't think so. "The results suggest the politician is wrong." Oh, yes, I love it! It's ... it's ... it's so right to be so wrong. Yes. And finally "the results are inconclusive." No, they're very conclusive. So here we're going to check our answer. Well done!
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Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.