Section II Response Questions in Test 1

A nutritionist for a school district would like to measure the BMI (body mass index) of fifth graders in the district. She randomly selects 25 fifth grade students from across the district and instructs their respective school nurses to measure their BMI.

Below is a stem-and-leaf table of the resulting BMIs:

(a) If a BMI of greater than 25 is considered overweight, what is the proportion of fifth graders in the sample that are considered overweight?

(b) The sample mean is 23.5 BMI, with a standard deviation of 4.8 BMI. Construct and interpret the 95% confidence interval of the mean BMI of fifth graders in the district.

(c) Is there statistical evidence that the mean BMI of all the fifth grade students in the district is greater than 25?

Suppose Mr. Jones keeps a large jar of jelly beans on his desk. He samples 35 jellybeans at random and weighs each of them on an analytic scale. The mean and standard deviation of the sample is 4.5 grams and 0.2 grams respectively.

(a) What is the 95% confidence interval of the mean weight of all the jellybeans in his jar?

(b) If the weight of all the jellybeans not including the jar is 950.4 grams, what is the 95% confidence interval of the total number of jelly beans in the jar?

A real estate agent would like to investigate the relationship between the sale price of a house and its lot size for a particular area. The following table shows sale and lot size data from a random sample of 24 houses recently sold in the area. Results from a regression analysis are also shown below.

(a) What is the intercept of the regression equation? Interpret this in the context of the problem.

(b) What is the correlation coefficient? Interpret this in the context of the problem.

(c) If the lot size of a house increases by 200 $\mathrm{ft}^2$, what is the predicted mean increase in sale price?

The dot plot below shows the field goal attempts (FGAs) of an NBA player for all games played in a particular season.

(a) Write a few sentences describing this distribution.

(b) If this player’s agent would like to address criticisms that his client shoots too much, which measure of central tendency should he emphasize? Explain.

(c) If the player played a total of 99 games that season, and 25 FGA’s and above is considered “shooting too much”, what percentage of these games did he shoot too much?

You and your friends play a game where a fair coin is tossed three times in a row and on each flip the player will either gain or lose points according to the table below.

(a) Construct a probability distribution table of the final scores of this game.

(b) What is the expected final score of this game?

(c) What is the probability that if a player plays the game 3 times, at least two of his final scores will be greater or equal to 5?

A new high-tech racing suit is developed for team USA speed skaters to be used in the Winter Olympic games. As part of the testing process before the games begin, the suit was given to 15 randomly selected speed skaters. The skaters were asked to skate a 5000m race wearing their regular suit and a 5000m race with the new suit. The results are summarized in the table below. Using the information in the “Improvement?” column, we would like to test the hypothesis that wearing the new suit will improve a skater’s 5000m race time.

(a) If we let $p$ be the proportion of skaters who improve their 5000m race time by wearing the suit, write a null and alternative hypothesis in terms of $p$ to test for this.

(b) Under the null hypothesis, use the binomial formula to calculate the probability of the observed data.

(c) Find the p-value of this significance test and state your conclusion.

(d) What would be the minimum sample size needed to reject the null in favor of the alternative for an observed improvement proportion no greater than the current sample proportion?