Confidence Interval CYU

You take sample of 200 M&Ms and find that 28 of them are red. What is the value of p̂ for this sample?

We call p̂ the point estimate for the population parameter p.

Mathematical Equivalence

ON

You take sample of 200 M&Ms and find that 28 of them are red. Based on your sample, you estimate that 14% of all M&Ms are red. Why can't we say that 14% of all M&Ms are red?

• The sample was not large enough.

• The point estimate will vary from one sample to another.

• The statistic never equals the parameter.

• People keep eating the red M&Ms.

Mathematical Equivalence

ON

• Because p̂ is the parameter.

• Because we want to know how much the p̂'s vary, not the p's.

• Because p̂ is a more accurate number than p.

• Because we only have p̂ since the only information we have is from our sample.

With a point estimate of p̂=0.14 and a margin of error of 0.0491, what is the lower end of the confidence interval?

Mathematical Equivalence

ON

With a point estimate of p̂=0.14 and a margin of error of 0.0491, what is the upper end of the confidence interval?

Mathematical Equivalence

ON

Our 95% confidence interval is (0.0909, 0.1891). What is this interval an estimate of?

• The proportion of M&Ms that get eaten.

• p=the population proportion of all M&Ms that are red.

• p̂=the sample proportion of M&Ms that are red.

• The proportion of red M&Ms in any sample of 200 M&Ms.

Which of these is the best explanation of what it means that our interval is a 95% confidence interval?

• There is a 95% chance that the interval contains the parameter we are estimating.

• If we were to construct an interval for every possible sample, 95% of the intervals would contain the statistic.

• If we were to construct an interval for every possible sample, 95% of the intervals would contain the parameter.

• 95% of the sampling distribution falls within the interval.