A social media company conducted a survey of n = 400 randomly selected users to see if they prefer the new interface. The survey results showed that 40% of the sample preferred the new design. Based on this, a 90% confidence interval was calculated as (0.35, 0.45).

Which of the following is the most accurate interpretation of this interval?

A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean distance for group 1 was 30 metres, with a standard deviation s_1 = 8 metres. The mean distance for group 2 was 26 metres, with a standard deviation s_2 = 6 metres. Assume the two groups of kicks are independent. Let \mu_1 and \mu_2 represent the mean distance we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium- and an air-filled football. Assume that two-sample t-procedures are safe to use.

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, one class of second grade children learns with the activities. Another class of second grade children serves as the control and learns without the activities. After some period of time, the reading skills of all of these children were assessed. A summary of these data is:

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. 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.

The appropriate hypotheses are

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.

We are interested in a 99% confidence interval for the population mean birth weight. The margin of error associated with the confidence interval 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 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.

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.