Learn how to perform one-proportion hypothesis tests and construct one-proportion confidence intervals on a Casio 9750 graphing calculator.
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1-Proportion Z Test and Confidence Interval
We're going to cover how to run a 1-proportion hypothesis test and calculate a 1-proportion confidence interval using a Casio fx-9750 calculator in the context of an example.
When to use proportions
We use a proportion when we are summarizing data that are categorical and can be grouped into two responses. For example, if we take a poll and the possible answers are yes and no, then we might example a proportion of people who responded a specific way.
We also need to make sure the conditions for using inference on the proportion are satisfied before we proceed with one of these tests or confidence intervals. For example, if we are conducting a confidence interval, we would need to make sure that there are at least 10 responses in each category.
Context
Suppose we were interested in determining whether more or fewer than 50% of Americans approved of the job the US Supreme Court was doing. We could summarize this as a hypothesis test. The null hypothesis is that the approval rating is 50%, and the alternative hypothesis is that the approval rating is different than 50%. We'll use a significance level of alpha equals 0.05.
According to a July 2014 Gallup poll, 47% of American adults approve of the job the Supreme Court is doing [ref]. The sample included data on 1,013 adults. Our two summaries here are a sample size of n = 1013 adults and a sample proportion of 0.47, which means we had 1,013 times 0.47, or about x = 476 people in the sample say that they approved of the job the Supreme Court is doing. We've verified the conditions for this sample are satisfied so that we can move ahead with conducting the hypothesis test.
Hypothesis test on calculator
To conduct a 1-proportion hypothesis test on the calculator,
go to Menu,
navigate to Stat,
hit F3 to go to open tests,
for proportions, we use a Z test, so hit F1, and finally,
choose 1-P for a 1-proportion hypothesis test.
Now we must specify the details for our hypothesis test. Looking at our hypotheses, note that the null value is p-not equals 0.5, and it is two-sided. So we make sure we have a not-equals sign. If we had needed to change to a different sided test, we could have used the keys F1, F2, or F3, and we'll here need to change p-not to 0.5 and hit execute. We also need to specify how many people's responses aligned with the category we are interested in, approval, which is 476 people in our sample. Finally, we specify the sample size, which was 1,013 adults. Once we've entered our data, we hit execute one more time to get the results of the hypothesis test.
The results show us several pieces of information:
we have an alternative hypothesis of p not-equal to 0.5,
our Z test statistic is -1.917,
the test's p-value is 0.055,
the sample proportion is 0.47, and
the sample size is 1,013.
Because the p-value is larger than alpha, we do not reject the null hypothesis. That is, we don't have strong evidence to conclude the approval rating is different than 50%.
When I'm done, I can exit out to the main Stat page.
Confidence interval
Suppose we had been interested in constructing a 95% confidence interval for the data instead of a hypothesis test for the data.
Go to INTR, for "confidence interval",
choose Z since we're working with proportions, and
choose 1-P for 1-proportion confidence interval.
Next, enter the confidence level of interest. We'll use 95%, which we write as 0.95. And then enter in our data. The calculator has, conveniently for us, already copied over the data summary from the hypothesis test. Finally, execute the test to get the interval.
Here is the left end of the interval, the right end, the center of the interval, which is also our sample proportion, and the sample size. So now we can write that we are 95% confident that the true proportion of US adults who approve of the job the Supreme Court is doing is between 43.9% and 50.1%.
16 сен 2024
