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.

During the recent century, some valleys in Western Australia have become heavily industrialised. The industries that operate there emit pollution that can change the level of acidity (measured as pH level) of rainwater that falls in the region. Scientists have long suspected that industrial pollution leads to more acidic rain (rain with lower pH level). Scientists know that before the industrial development of the region, the rainwater falling in that region had an average pH level of 6.3, with standard deviation 0.45. Recently, a study of rainwater collected in the region involved 39 samples of rainwater. The scientists observed a sample mean pH of 6.1. The research question here is: Can scientists conclude that the average pH level for rain in this region is lower now than it was before heavy industry arrived?

In formulating hypotheses for a statistical test of significance, the alternative hypothesis is often