Point Estimates Lets explore n Find a point

Point Estimates

Let’s explore n Find a point estimate of the area of the rectangles on the page. ¨ How many should we sample? ¨ Use Math – PRB – Rand. Int(1, 100, n)

Questions n Do all of your trials contain the true mean of 7. 4? n What’s the shape of the graph? n If mean is 7. 4 and standard deviation is 5. 126 , what is the mean & standard deviation of the sampling distribution?

Point Estimate n It is a single number that is based on sample data that represents a plausible value of the characteristic for the population. n It’s the statistic (from a sample) that we use to estimate the parameter (of the population).

Examples n To find a point estimate of the average height of students in this class I could use a sample of 10 people and find their average height. n To find the percent of green M&M’s in a bag, I could use 20 bags and find the average percent in those bags to estimate the true population proportion.

An article on affirmative action reported that 537 of the 1013 people surveyed believed that affirmative action programs should be continued. Find a point estimate of the population proportion. n Point estimate of p is: n Based on the sample, we estimate that 53% believe that affirmative action should continue.

Calories per ½ cup serving for 16 popular chocolate ice cream is shown below. Find a point estimate for the number of calories in a serving of chocolate ice cream. 270 160 199 160 150 180 150 140 160 290 170 110 170

Calories per ½ cup serving for 16 popular chocolate ice cream is shown below. Find a point estimate for the number of calories in a serving of chocolate ice cream. We could use the 270 160 199 160 150 180 150 140 160 290 170 110 170 mean: median:

Calories per ½ cup serving for 16 popular chocolate ice cream is shown below. Find a point estimate for the proportion that are greater than 190. 270 160 199 160 150 180 150 140 160 290 170 110 170

We tend to pick an estimate that yields an accurate estimate. n To estimate a proportion – we use a proportion (not a mean). n To estimate how many – we use the mean, median, or trimmed mean n To estimate variation – we use standard deviation, variance, or range

For our class (the population), find a point estimate for the … n Average height n Difference between height of girls & height of the boys n Proportion with brown eyes

Unbiased Statistic n It’s a statistic whose mean value is equal to the value of the population being estimated. n Biased – not equal to the population being estimated.

Examples of unbiased estimators n mean: median trimmed mean n Proportion: n Variance:

Biased: Range n If using a sample – it will only equal the population if you have the lowest & highest values. The probability for this to happen is very small – almost 0. n Thus it’s biased because for most, the sample range is smaller than the population range.

Airborne Times: 57, 54, 55, 51, 56, 48, 52, 51, 59. Find point estimate of mean & variance. Put them in list 1 n Do 1 -var Stat n To get the variance, you must take the st. dev. (Sx) and square it. n

Homework n Page 481 (1 -4, 25, 26)