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.

The standard error of the sample mean is:

Do students tend to improve their maths SAT scores the second time they take the test? A random sample of four students who took the test twice received the following scores:

Assume that the change in maths SAT score (second score – first score) for the population of all students taking the test twice is Normally distributed, with mean μ.

The appropriate hypotheses are

A special diet is intended to reduce the cholesterol of patients at risk of heart disease. If the diet is effective, the target is to have the average cholesterol of this group be below 200. After six months on the diet, an SRS of 50 patients at risk for heart disease had an average cholesterol of 192, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume the distribution of the cholesterol for patients in this group is approximately Normal with mean μ.

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

Which of the following is an example of a matched pairs design?

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The appraised values of three recently sold studio apartments in Melbourne are (in thousands of dollars) 160, 215, and 195. 

The standard error of the mean of these three appraised values is

An engineer designs an improved automobile engine for a certain make of automobile. The previous design had an average highway petrol consumption of 10 l/km (litres per 100 kilometres) with a standard deviation of 0.5 l/km. The new engine has an average highway petrol consumption of 9.8 l/km, based on a sample of 3600 cars of the model with the new engine. Although the difference is quite small, the effect is statistically significant. The explanation is

A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes, with P-value = 0.287. This means

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean μ, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses

H0: μ = 115

Ha: μ ≠ 115.

The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students.