Unit Test — Unit test Answers

In an effort to improve scores on college-entrance exams, the principal at a large high school chooses 35 students at random who have already taken the exam. The students are enrolled in a six-week prep course to improve their scores. After the prep course, the students take the college-entrance exam again. The mean difference (first – second) in exam scores is –1.75 points with a standard deviation of 7.12 points. Assuming the conditions for inference are met, what is the test statistic for testing the hypotheses ?

A company that sells hair-care products wants to determine if a product that combines shampoo and conditioner works better than a shampoo and conditioner used separately. A researcher recruits 60 volunteers and pairs them according to age, hair color, and hair type. For each pair, the researcher flips a coin to determine which volunteers will use the shampoo/conditioner combination and which ones will use the separate shampoo and conditioner. After using the products for one month, the subjects are asked to rate their satisfaction with the hair products on a scale of 1–10 (1 = highly dissatisfied and 10 = highly satisfied).

On a college entrance exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The counselor would like to know if there is convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses = 25 versus < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value?Find the t-table here.

The distribution of the heights of five-year-old children has a mean of 42.5 inches. A pediatrician believes the five-year-old children in a city are different. The pediatrician selects a random sample of 40 five-year-old children and measures their heights. The mean height of the sample is 41.7 inches with a standard deviation of 3.3 inches. A significance test at an alpha level of produces a P-value of 0.133. What is the correct interpretation of the P-value?