OpenIntroOrg 1-Sample Hypothesis Test and Confidence Intervals using Casio fx-9750GII

Learn how to perform one-sample hypothesis tests and construct one-sample confidence intervals on a Casio 9750 graphing calculator.

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Approximate audio script:

1-sample t test / CI (and Z test / CI)

I'll cover how to construct a confidence interval and run a hypothesis test for a single mean using a Casio fx-9750 graphing calculator in the context of an example.

Context

I'll consider data about mercury content in dolphins. Dolphins are near the top of the oceanic food chain, which causes dangerous substances such as mercury to concentrate in their organs and muscles. This is an important problem for both dolphins and other animals, like humans, who occasionally eat them.

The data set comes from a study where 19 Risso's dolphin meat samples were tested. The average concentration was 4.4 micrograms of mercury per gram of meat. The sample standard deviation was 2.3, and the data ranged from 1.7 to 9.2.

Confidence interval

I'll construct a confidence interval based on the sample. To begin, I navigate to the Stat section through the menu, go to INTR for confidence interval, choose T, and then choose 1-S for 1-sample of numerical data. I'll be using summary statistics, so I'll select Var. Next, I specify the confidence level, and I'll use 90%. Then I enter the mean [pause], standard deviation [pause], and sample size. Alternatively, if I had raw data, I could enter that data into one of the lists and then specify the list I'd like to use, which is covered in the 2-sample inference video. Finally, when I'm done, I hit execute to get results.

The results page confirms that I've constructed a 90% confidence interval, and that the interval runs from 3.49 [pause] to 5.31.

Based on these results, I'm 90% confident the true average mercury content of muscles in Risso’s dolphins is between 3.49 and 5.31 micrograms of mercury per gram of meat. Note that this is above the Japanese regulation level of 0.4.

Now that I've completed the confidence interval, I can exit out to the main Stat page.

Hypothesis test

Had I instead wanted to run a hypothesis test, I could have, instead of choosing INTR, chosen TEST for hypothesis test. I again would select T and 1-S. Suppose I wanted to test a one-sided hypothesis to evaluate whether the mercury content exceeds the legal standard of 0.4, which I'll test at a 0.05 significance level. I would first specify the sidedness of the alternative hypothesis: here I choose greater than, since I'll be checking whether the population mean is above a certain threshold. Next, I specify the null value, which is the legal limit of 0.4. Finally, I enter the data. Here, the data from the confidence interval has already been duplicated over to the hypothesis test, so I hit execute to return results.

I can confirm the alternative hypothesis matches what I specified earlier. The test statistic is 7.58. The p-value is 2.6e-07, which is in scientific notation. To put this into standard decimal form, I could write 2.6 and then, since it is e-negative-7, move the decimal to the left by 7 spots. Following the p-value, summary information for the sample is provided.

I use the p-value to evaluate the hypothesis test, and since the p-value is smaller than the significance level, alpha, I reject the null hypothesis and conclude that, on average, Risso's dolphin meat exceeds the legal mercury limit in Japan, which is consistent with our confidence interval from earlier.

Remarks

One last quick note: in the rare case where the standard deviation for the population is known and not estimated using our sample -- that is, if I know sigma -- then I would choose a Z confidence interval or a Z test instead of a T confidence interval or t test.

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1-Sample Hypothesis Test and Confidence Intervals using Casio fx-9750GII
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