Question

Each of the following situations describes a normally distributed population for which a statistical procedure should be used. Match each situation with the appropriate procedure to use.

Gale is obsessed with creating a reliable method of brewing the perfect cup of coffee. She wants to determine the likely range of weight of whole coffee beans from her trusty two-tablespoon scoop. She measures the weight of a sample of 15 scoops, finding that they average 17 g.


Shannon is studying IQ scores, which are normally distributed with a mean of 100. She believes that the mean IQ of classical musical composers is at least 112 and tests this belief with a random sample of 20 composers.


Jason wants to estimate what the balance of his retirement account will be in one month. All of the money in his account is allocated in an S&P 500 Index Fund. From 1950 to 2015, he calculates this index has had an average monthly return of 0.69% with a standard deviation of 4.15%.


Ted is investigating whether a rugby team has systematically violated the rules during a season. He obtains pressure-gauge readings of a random sample of 16 balls used throughout the season to test whether the average pressure of that team's rugby balls was below the minimum 9.5 psi dictated by the Rugby Union. The league supplies him with the league mean and standard deviation of ball pressures.

Possible Answers Include:

*one-sample t-confidence interval for the mean

*one-sample t-Test for a mean

*one-sample z-Test for a mean

*one-sample z-confidence interval for the mean

Answer 1

1. Since, the sample size is small (<30), we go for t-test. Since Gale wants to determine the likely range of weight of whole coffee beans, we go for one-sample t-confidence interval for the mean

2. Since, the sample size is small (<30), we go for t-test. Since Shannon is trying to prove mean of one set of samples we go for one-sample t-Test for a mean

3. Since, the sample size is large (>30), we go for Z-test. Here, Jason in trying to figure out his retirement balance which is an estimate. Hence, we go for one-sample z-confidence interval for the mean

4. Since, the sample size is small (<30) but we know the population variance (league mean and standard deviation of ball pressures), we go for Z-test. Since Ted is investigating whether a rugby team has systematically violated the rules during a season and has mean of samples, we go for one-sample z-Test for a mean