Table of Contents

## Which of the statistics appear to be unbiased estimators of the population parameter?

Statistics A, C, and D appear to be unbiased. This is indicated by the fact that the mean of the estimated sampling distribution for each of these statistics is about 75, the value of the true population parameter.

**Is there a formula sheet for AP stats?**

If you’re going to be taking the AP Statistics exam, you’re in luck! During the test, you’ll have access to a formula sheet that has many useful equations.

### Are sufficient funds available to estimate the mean stopping distance to within 2 feet of the true mean stopping distance with 95% confidence explain your answer?

Sufficient funds are not available. It is not possible to estimate the true mean stopping distance to within 2 feet with 95% confidence for $12,000.

**Is the variability in sugar content of the cereals similar or different for the three shelves?**

There is more variability (larger range and larger IQR) for the one-cup cereals. The shapes of the two distributions differ. The distribution of sugar content for three-quarter-cup cereals is reasonably symmetric: notice that the median is in the middle of the box.

## What is an unbiased estimator of the population mean?

A statistic is called an unbiased estimator of a population parameter if the mean of the sampling distribution of the statistic is equal to the value of the parameter.

**Is there a significant difference in the mean amount of E coli bacteria detected by the two methods for this type of beef?**

We do NOT have statistically significant evidence to conclude that there is a difference in the mean amount of E. coli bacteria detected by the two methods for this type of beef. In other words, there does not appear to be a significant difference in these two methods for measuring the level of E.

### How do you find the probability of A and B?

Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B). If the probability of one event doesn’t affect the other, you have an independent event. All you do is multiply the probability of one by the probability of another.

**What is the 70th percentile of the distribution of stopping distances?**

128.4 feet

Thus, the 70th percentile value can be computed as: X= 4x +zo y = 125 +0.52(6.5) = 128.4 feet. Part (b): From part (a), it was found that a stopping distance of 128.4 feet has a cumulative probability of 0.70.

## What are approximate values in cents per gallon of the median and interquartile range of the new distribution of combined gasoline taxes?

The median is approximately 21 cents per gallon. The first and third quartiles are approximately 18 cents per gallon and 25 cents per gallon, respectively. The IQR is Q3 – Q1, which is approximately 25 – 18 = 7 cents per gallon.

**What is the point estimate for P?**

After observing the BT, the researcher counts the number of successes, x, in the n BT. We define p = x/n, the proportion of successes in the sample, to be the point estimate of p. For example, if I observe n = 20 BT and count x = 13 successes, then my point estimate of p is p = 13/20 = 0.65.