During routine screening, a doctor notices that 22% of her adult patients show higher than normal levels of glucose in their blood – a possible warning signal for diabetes. Hearing this some researchers decide to conduct a large scale study hoping to estimate the proportion to within 4% accuracy with 98% confidence. How many randomly selected adults must they test?

Proportion sample size

A random sample of 337 college students was asked whether or not they were registered to vote. We wonder if there is an association between a student’s sex and whether the student is registered to vote. The data are provided in the table below. Men Women Total Registered 104 147 251 Not Registered 33 53 86 137 200 337

Chi-square test for independence

According to a June 2004 Gallup poll, 28% of Americans “said there have been times in the last year when they haven’t been able to afford medical care.” Is this proportion higher for black Americans than for all Americans? In a random sample of 801 black Americans, 38% reported that there had been times in the last year when they had not been able to afford medical care. Test an appropriate hypothesis and state your conclusion.

1 proportion z-test One tail

Before you took this course, you probably heard many stories about intro stats courses. Oftentimes parents of students have had bad experiences with intro stats courses and pass on their anxieties to their children. To test whether actually taking intro stats decreases students’ anxieties about statistics, a statistics instructor gave a test to rate student anxiety at the beginning and end of his course. Anxiety levels were measured on a scale of 0-10. The following table contains the data for 16 randomly chosen students from a class of 180 students. Does the data indicate that anxiety levels about statistics decreases after students take an intro stats course? Test an appropriate hypothesis and state your conclusion. Pre-course anxiety level 7 6 9 5 4 3 2 1 Post-course anxiety level

The difference of means –dependent samples One tail

As part of a survey, students in a large introductory statistics class were asked whether or not they ate breakfast that morning. Does it appear eating breakfast or not is different for the two genders? Test an appropriate hypothesis. The data appears in the following table: breakfast No breakfast total Male 66 132 Female 125 74 199 Total 191 140 331

Chi-square test of homogeneity

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. The insurance company knows that, last year, the life expectancy of its policyholders was 77 years. They want to know if their clients this year have a longer life expectancy, on average, so the company randomly samples some of the recently paid policies to see if the mean life expectancy of policyholders has increased. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. Does this sample indicate that the insurance company should change its premiums because life expectancy has increased? Test an appropriate hypothesis and state your conclusion. 86 75 83 84 81 77 78 79 76 85 70 73 74 72

1 mean t-test One tail

In 2000, the United Nations claimed that there was a higher rate of illiteracy in men than in women from the country of Qatar. A humanitarian organization went to Qatar to conduct a random sample. The results revealed that 45 out of 234 men and 42 out of 251 women were classified as illiterate on the same measurement test. Do these results indicate that the United Nations findings were correct? Test an appropriate hypothesis and state your conclusion.

2-proportion z-test One tailed

A biology professor reports that historically grades in her introductory biology course have been distributed as follows: 15% A’s, 30% B’s, 40% C’s, 10% D’s, and 5% F’s. Test an appropriate hypothesis to decide if the professor’s most recent grade distribution (given below) matches the historical distribution. Grade A B C D F Frequency 89 121 78 25 12

Chi-square goodness of fit