Let's first check whether the conditions that allow us to safely use the two-sample t-test are met.Here, 239 students were chosen and were naturally divided into a sample of females and a sample of males. Since the students were chosen at random, the sample of females is independent of the sample of males.Here we are in the second scenario — the sample sizes (150 and 85), are definitely large enough, and so we can proceed regardless of whether the populations are normal or not.Tip: Alternative versions are available, click the arrow to switch. In order to avoid tedious calculations, we use Excel to find the test statistic. In this case, Excel gives us a t-value of -4.66.Just for this first example, let's make sure that we understand what the ingredients are that go into the test statistic calculation and how we use them to find the test statistic.Learn By DoingBearing in mind that sample 1 is the sample of females, and sample 2 is the sample of males, according to the output:n1 =  n2 =  y1-bar =  y2-bar =  s1 =  s2 =

teacher is experimenting with a new computer-based instruction and conducts a study to test its effectiveness. In which situation could the teacher use the two-sample t-test for comparing two population means? The teacher gives each student in the class a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a post-test. The teacher wants to compare test scores for each student to see whether the data will show an improvement. The teacher randomly divides the class into two groups. One of the groups receives computer-based instruction and the other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the test scores of the two groups. The teacher uses a combination of traditional methods and computer-based instruction. She asks students which they liked better. She wants to determine if the majority prefer the computer-based instruction.

Which of these examples of samples is appropriate for a paired t-test?Question 7Answera.The pupils in a boys’ school, and in a girls’ school in the same townb.Pairs of same-gender twinsc.Sets of two people solving word puzzles together over the internetd.Surveys given to a group of fathers and their oldest child

The t test for the difference between the means of two independent populationsalways assumes that the respectivea. sample sizes are equalb. sample variances are equalc. populations are normally distributed if each sample size is less than 30d. All of the above

The owner of a test prep company was interested in whether students who took the company’s face to face test prep class did better on the GRE (a standardized test required for admission to many graduate programs) than students who followed the test prep company’s live online program. The live online test prep class met in an online classroom with live video instruction for the same number of hours as the face to face class. In which situation could the test prep company use the two-sample t-test for comparing two population means? The test prep company randomly divides the students into two groups. One of the groups receives the face to face test prep class and the other group receives the live online test prep class. After completing their test prep course, each student takes the GRE and the test prep company compares the test scores of the two groups. The students take part of their GRE test prep course online and the remaining part in the face to face method. The test prep company asks the students which they liked better. The company wants to determine if the majority prefer the online class. The test prep company gives each student a pretest. Then each student completes the live online test prep class. Afterwards, each student takes a posttest. The test prep company wants to compare the pretest and posttest GRE scores for each student to see whether the data will show an improvement.

College Students and Drinking Habits: A public health official is studying differences in drinking habits among students at two different universities. They collect a random sample of students independently from each of the two universities and ask each student how many alcoholic drinks they consumed in the previous week.The official conducts a two-sample t-test to determine whether these data provide significant evidence that students at University 1 drink more than students at University 2. The test statistic is t = 2.64 with a p-value 0.005.Which of the following is an appropriate conclusion? The samples provide significant evidence that students at University 1 drink more than students at University 2. The samples do not provide statistically significant evidence that there is a difference in drinking habits at the two universities. We cannot use the t-test in this case because the variables (number of drinks) are likely skewed to the right at each university.