Confidence Interval Estimation for a Population Mean Lecture 36 Section 10 4 Mon Nov 5 2007 Confidence Intervals To estimate we will use confidence intervals as we did when estimating p The basic form as well as the theory is the same as before pt est appropriate no of st devs Confidence Intervals What is the point estimate for What is the standard deviation for this estimator How do we determine the appropriate number of standard deviations Confidence Intervals The confidence interval will be x z n or or s x z n s x t n When to Use Z If The population is normal or nearly normal and is known or The population is not normal but the sample size is at least 30 Then use Z When to Use t If The population is normal or nearly normal and is not known Then use t Example Example 10 4 p 641 Construct a 95 confidence interval for the true mean weight of such boxes Example Use Z Why n 25 x 9 82 Assume that 0 29 Why Level of confidence 95 so z 1 96 Example The confidence interval is 0 29 9 82 1 96 9 82 0 114 25 9 706 9 934 TI 83 Confidence Intervals When the standard normal distribution applies do the following Press STAT Select TESTS Select ZInterval A window appears requesting information TI 83 Confidence Intervals Select Data or Stats Assume we selected Stats Enter Enter x Enter n Enter the level of confidence Select Calculate and press ENTER TI 83 Confidence Intervals A window appears containing The title ZInterval The confidence interval in interval notation The sample mean The sample size Example Example 10 5 p 643 Construct a 99 confidence interval for the mean number of unoccupied seats Example Should we use Z or t Why n 61 x 12 6 s 4 4 Level of confidence 99 Find t Example The confidence interval is 4 4 12 6 2 660 12 6 1 499 61 11 101 14 099 TI 83 Confidence Intervals To use t do the following Press STAT Select TESTS Select TInterval A window appears requesting information TI 83 Confidence Intervals Select Data or Stats Assume we selected Stats Enter x Enter s Enter n Enter the level of confidence Select Calculate and press ENTER TI 83 Confidence Intervals A window appears containing The title TInterval The confidence interval in interval notation The sample mean The sample standard deviation The sample size
View Full Document
Unlocking...