You are thinking of employing a t-procedure to test hypotheses about the mean of a population using a significance level of 0.05. You suspect the distribution of the population is not Normal and may be moderately skewed.

Which of the following statements is correct?

We wish to see if, on average, traffic is moving at the posted speed limit of 100 km per hour along a certain stretch of Interstate highway. On each of four randomly selected days, a randomly selected car is timed and the speed of the car is recorded. The observed speeds are 105, 100, 105, and 110 km per hour.

Assuming that speeds are Normally distributed with mean μ, we test whether, on average, traffic is moving at 100 miles per hour by testing the hypotheses

Based on these data (obtain summary statistics and do the test of significance),

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.

We wish to see if, on average, traffic is moving at the posted speed limit of 100 km per hour along a certain stretch of an interstate highway. On each of four randomly selected days, a randomly selected car is timed and the speed of the car is recorded. The observed speeds are 105, 100, 105, and 110 km per hour.

Assuming that speeds are Normally distributed with mean μ, we test whether, on average, traffic is moving at 100 km per hour by testing the hypotheses

The water diet for weight loss requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in kilograms) are

For the population of all adults, assume that the weight loss after six weeks on the diet (weight before beginning the diet – weight after six weeks on the diet) is Normally distributed with mean μ.

The appropriate hypotheses are

The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in kilograms) are

For the population of all adults, assume that the weight loss after six weeks on the diet (weight before beginning the diet – weight after six weeks on the diet) is Normally distributed with mean μ.

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. It would be interesting to see if this is 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.

A 95% confidence interval for the average cholesterol of patients at risk for heart disease who have been on the diet for six months is closest to

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 0.21 kg. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with some mean μ. What is a 90% confidence interval for the population mean birth weight based on these data?

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, a simple random sample of 50 patients at risk for heart disease had an average cholesterol of 192, with standard deviation s = 21. Assume the distribution of the cholesterol for patients in this group is approximately Normal with mean μ. A statistical test is conducted to determine if there is sufficient evidence that the diet is effective in meeting the target. 

The appropriate degree of freedom for this test is .

The height (in cm) of males in Australia is believed to be Normally distributed, with mean μ. The average height of a random sample of 50 Australian adult males is 177.1 cm, with a sample standard deviation of 10.7 cm. What is the standard error of the sample mean?