**Example 1:**

If 60% of a sample of 120 individuals leaving a diner claim to have spent over $12 for lunch, determine a 99% confidence interval estimate for the proportion of patrons who spent over $12.

**sqrt(.4 * .6/ 100)**

*[1] 0.04898979*

**z <- qnorm(.005, lower.tail=FALSE) * 0.04898979**

# .005 is due to our test containing 2 tails #

**.60 + c(-z, z)**

*[1] 0.4738107 0.7261893*

Conclusion: We are 99% certain that the proportion of diner patrons spending over $12 for lunch is between 0.4738107 (47.34%) and 0.7261893 (72.62%).

**Example 2:**

In random sample of lightbulbs being produced by a factory, 20 out of 300 were found to be shattered during the shipping process. Establish a 95% confidence interval estimate that accounts for these damages.

**p = 20/300**

*[1] 0.06666667*

**sqrt(.066 * .934 / 100)**

*[1] 0.02482821*

**z <- qnorm(.025, lower.tail=FALSE) * 0.02482821**

**0.06666667 + c(-z,z)**

*[1] 0.01800427 0.11532907*

Therefore, we can be 95% certain that the proportion of light bulbs damaged during the shipping process is between 0.01800427 (1.80% and 11.53%).

Furthermore, if we wished, we could apply these ratios to a total shipment to create an estimation.

If 1000 light bulbs shipped, we can be 95% confident that between 18 and 115.3 light bulbs are damaged within the shipment.

In the next article, we will be discussing hypothesis tests. Until then, stay tuned Data Monkeys!

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