# 8.2 A single population mean using the student t distribution  (Page 3/21)

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## Try it

You do a study of hypnotherapy to determine how effective it is in increasing the number of hourse of sleep subjects get each night. You measure hours of sleep for 12 subjects with the following results. Construct a 95% confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data.

8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5

(8.1634, 9.8032)

The Human Toxome Project (HTP) is working to understand the scope of industrial pollution in the human body. Industrial chemicals may enter the body through pollution or as ingredients in consumer products. In October 2008, the scientists at HTP tested cord blood samples for 20 newborn infants in the United States. The cord blood of the "In utero/newborn" group was tested for 430 industrial compounds, pollutants, and other chemicals, including chemicals linked to brain and nervous system toxicity, immune system toxicity, and reproductive toxicity, and fertility problems. There are health concerns about the effects of some chemicals on the brain and nervous system. [link] shows how many of the targeted chemicals were found in each infant’s cord blood.

 79 145 147 160 116 100 159 151 156 126 137 83 156 94 121 144 123 114 139 99

Use this sample data to construct a 90% confidence interval for the mean number of targeted industrial chemicals to be found in an in infant’s blood.

## Solution b

Enter the data as a list.
Press `STAT` and arrow over to `TESTS` .
Arrow down to `8:TInterval` and press `ENTER` (or you can just press `8` ). Arrow to Data and press `ENTER` .
Arrow down to `List` and enter the list name where you put the data.
Arrow down to `Freq` and enter 1.
Arrow down to `C-level` and enter 0.90
Arrow down to `Calculate` and press `ENTER` .
The 90% confidence interval is (117.41, 137.49).

## Try it

A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week. The responses are recorded in [link] . Use this sample data to construct a 98% confidence interval for the mean number of hours statistics students will spend watching television in one week.

 0 3 1 20 9 5 10 1 10 4 14 2 4 4 5

## Solution b

Enter the data as a list.
Press `STAT` and arrow over to `TESTS` .
Arrow down to `8:TInterval` .
Press `ENTER` .
Arrow to `Data` and press `ENTER` .
Arrow down and enter the name of the list where the data is stored.
Enter `Freq` : 1
Enter `C-Level` : 0.98
Arrow down to `Calculate` and press `Enter` .
The 98% confidence interval is (2.3965, 9,8702).

## References

“America’s Best Small Companies.” Forbes, 2013. Available online at http://www.forbes.com/best-small-companies/list/ (accessed July 2, 2013).

Data from Microsoft Bookshelf .

Data from http://www.forbes.com/.

“Disclosure Data Catalog: Leadership PAC and Sponsors Report, 2012.” Federal Election Commission. Available online at http://www.fec.gov/data/index.jsp (accessed July 2,2013).

“Human Toxome Project: Mapping the Pollution in People.” Environmental Working Group. Available online at http://www.ewg.org/sites/humantoxome/participants/participant-group.php?group=in+utero%2Fnewborn (accessed July 2, 2013).

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