Exam 1: Introduction to Statistics

A gardener has 75 clients, 45% of whom are businesses. Find the number of business clients.

The table shows the weights (in pounds) and monthly incomes (in dollars) of nine randomly selected women between the ages of 18 and 65. Assume that the x-values are the weights and the y-values are the monthly incomes. What i Weight (lb) 113 132 155 122 166 140 118 129 185 Monthly Income (dollars) 1420 3650 5475 2310 4710 2910 1720 2460 4115 ssue can be addressed by conducting a statistical analysis of the values?

"7 out of 10 dentists recommend Brand X toothpaste". This finding is based on the results of a survey of 10 randomly selected dentists. What is wrong with this survey?

A researcher published this survey result: "74% of people would be willing to spend 10 percent more for energy from a non-polluting source". The survey question was announced on a national radio show and 1,200 listeners responded by calling in. What is wrong with this survey?

A T.V. show's executives commissioned a study to gauge the impact of the show's ratings on the sales of its advertisers.

Identify the type of observational study (cross-sectional, retrospective, prospective). -A researcher conducts an experiment to determine whether acupuncture can help people to recover from back injuries. Participants are randomly assigned to a treatment group or a control group. Over a period of three weeks, those assigned to the treatment group receive acupuncture treatments. At the end of the three weeks, the improvement reported by those in the treatment group is compared with the improvement reported by those in the control group. In this experiment there is no blinding. What does this mean and why could this cause a problem?

In a study of headache patients, every one of the study subjects with a headache was found to be improved after taking a week off of work. Conclusion: Taking time off work cures headaches.

Determine which of the four levels of measurement is most appropriate. Students' grades, A, B, or C, on a test.

Form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or make subjective judgments about the results. Last year, the average math SAT score for students at one school was 475. The headmaster introduced new teaching methods hoping to improve scores. This year, the mean math SAT score for a sample of students was 481. Is there statistically significant evidence that the new teaching method is effective? If the teaching method had no effect, there would be roughly a 3 in 10 chance of seeing such an increase. Does the result have statistical significance? Why or why not? Does the result have practical significance?

The table shows the weights (in pounds) and monthly incomes (in dollars) of nine randomly selected women between the ages of 18 and 65. Assume that the x-values are the weights and the y-values are the monthly incomes. If we use statist Weight (lb) 113 132 155 122 166 140 118 129 185 Monthly Income (dollars) 1420 3650 5475 2310 4710 2910 1720 2460 4115 ical methods to conclude that there is a correlation (or relationship or association) between the weights of women and their monthly incomes, can we conclude that by increasing her weight a woman can increase her monthly income?

On a test, 74% of the questions are answered correctly. If 111 questions are correct, how many questions are on the test?

Given the data in the table, what issue can be addressed by conducting a statistical analysis of the values? Amounts of Saturated Fat (in grams) in Two-Once Regular and Low-Fat Muffins Regular 4.5 3.5 3.7 5.2 4.9 3.9 Low-Fat 1.2 2.1 2.2 1.8 1.6 2.2

Identify which type of sampling is used. A pollster uses a computer to generate 500 random numbers, then interviews the voters corresponding to those numbers.

Identify the type of observational study (cross-sectional, retrospective, prospective). -A researcher obtains a sample of high school teachers in his school district by randomly selecting 10 high schools and interviewing all the teachers at each of these 10 schools. What kind of sampling is being used here? Will the resulting sample be a simple random sample of the population of teachers in the school district? Explain your thinking.

Why do you think that cluster sampling is frequently used in practice?

Identify the type of study used. A town obtains current employment data by polling 10,000 of its citizens this month.

The table shows the weights (in pounds) and monthly incomes (in dollars) of nine randomly selected women between the ages of 18 and 65. Assume that the x-values are the weights and the y-values are the monthly incomes. Are the x Weight (lb) 113 132 155 122 166 140 118 129 185 Monthly Income (dollars) 1420 3650 5475 2310 4710 2910 1720 2460 4115 -values matched with the corresponding y-values? That is, is each x-value associated with the corresponding y-value in some meaningful way? If the x- and y-values are matched, does it make sense to use the difference between each x-value and the y-value that is in the same column? Why or why not?

Subscribers of the women's magazine Cosmopolitan are asked to participate in a survey about preferred cereals for breakfast. Are the results likely to be representative of all women? Of all subscribers of Cosmopolitan? Why or why not?

An airline company advertises that 100% of their flights are on time after checking 5 randomly selected flights and finding that these 5 were on time. What is wrong with their claim?

Use the data in the table to answer the question. The x-values are amounts of saturated fat (in grams) in various regular two-ounce muffins. The y-values are amounts of saturated fat (in grams) in various "low fat" two-ounce muffins. Amounts of Saturated Fat in Regular and Low-Fat Muffins 4.7 6.1 3.5 5.2 3.8 4.3 1.2 2.1 0.8 1.5 1.8 2.4 The measured amounts of saturated fat were supplied by the producers of the muffins. Is there an incentive for producers to report values that are not accurate?