Lab Activity 3 | Math 113 | Name : ___________________ |

10 pts | Intro to Applied Stats |

**Materials Needed:**

Watch with second hand

The atomic clock at the National Institute of Standards and Technology in Boulder, Colorado, is considered to be the correct time.

- Record the deviation of your watch from the atomic clock in the table. Record your value in seconds. Use a positive value is your watch is fast and a negative value if your clock is slow.
- Synchronize your watch to the atomic clock. If you can't adjust yours, then note the difference and adjust all other times by that difference.
- Find at least nine (fifteen if you do this in a group) other people with watches with second hands and record (in seconds) their deviations from the atomic clock. You may wish to write their time and the actual time on another piece of paper and do the calculations later. This way, you don't use much of their time.

- Find a point estimate for the mean error and the standard deviation of the errors (error in this sense means the deviation from the actual time).
- Compute the mean, variance, and standard deviation for your values.
- Construct a 80%, 90%, 95%, and 99% confidence interval for the true population error.

Confidence Level | Critical Value | Maximum Error | Confidence Interval | |

from | to | |||

80% | ||||

90% | ||||

95% | ||||

99% |

- Do any of the confidence intervals contain zero?
- What would it mean if a confidence interval contained zero?
- As the level of confidence increases, what happens to the width of the confidence interval?

Suppose that a larger study wanted to be done to analyze this time problem. Your results can be used as a previous study to have an estimate of the population variance (necessary to estimate sample size). Use your sample variance as the estimate for the population variance.

- Determine how large of a sample would be necessary to obtain the level of confidence and maximum error of the estimate (in seconds) indicated in the table. Record each sample size in the table.

Level of Confidence | |||

Maximum Error |
90% | 95% | 99% |

30 seconds | |||

15 seconds | |||

5 seconds |

- As the maximum error of the estimate decreases, what happens to the sample size?
- What can be done to the confidence level to reduce the sample size?
- What can be done to the maximum error of the estimate to reduce the sample size?