Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, five rooms were carpeted and five were left uncarpeted. The rooms are similar in size and function. After a suitable period of time, the concentration of bacteria in the air was measured (in units of bacteria per cubic metre) in all of these rooms. The data and summaries are provided:

A psychologist has developed a set of activities intended to help children develop better reading skills. In a study of the effectiveness of these activities, four classes of second grade children in a public school were invited to participate and the activities were conducted by their respective teachers. Two of the classes (A and B) learn with the activities. The other two classes (C and D) serve as the control and learn without the activities. After some period of time, the reading skills of all of these children were assessed. A summary of these data is:

Do SAT coaching classes work? Do they help students to improve their test scores? In a study, eight students took a SAT exam a second time. Four of these students took an SAT coaching class. The other four students did not.  The improvements in test scores over the first exam were recorded for each group.

To analyse this data, we should use

Bags of a certain brand of tortilla chips claim to have a net weight of 140 grams. Net weights actually vary slightly from bag to bag and are Normally distributed with mean μ. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses

The one sample t statistic from a sample of n = 25 observations for the one-sided test of

H0: μ = 9, Ha: μ > 9

To estimate μ, the mean salary of lecturers at Australian colleges and universities, you obtain the salaries of a random sample of 400 lecturers. The sample mean is $73,220, and the sample standard deviation is $4400.

Scores on the SAT Mathematics test (SAT-M) are believed to be Normally distributed, with mean μ. The scores of a random sample of three students who recently took the exam are 550, 620, and 480. A 95% confidence interval for μ based on these data is

[hint: You need to first find the sample mean and sample standard deviation]

An SRS of 20 recent birth records at the local hospital were selected. In the sample, the average birth weight was 3.44 kg and the standard deviation was 0.21kg. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with some mean μ.

We are interested in a 95% confidence interval for the population mean birth weight. The margin of error associated with the confidence interval is:

A snack food producer produces bags of peanuts labelled as containing 30 grams. The actual weight of peanuts packaged in individual bags is Normally distributed with mean μ and standard deviation σ = 0.2 grams.   As part of quality control, n bags are selected randomly and their contents are weighed. The hypotheses of interest are H0: μ = 30 grams, Ha: μ ≠ 30 grams.