Kelsey Matthau is an advisor for a high school. The high school offers a class for students preparing to take college admissions exams. Kelsey is looking for evidence that the population mean score of students who attend the college admissions class is greater than the population mean score of students who do not attend. Since the school has every student take the exam during school hours, Kelsey has access to the students' scores. Using information from past years, she assumes that the population standard deviation is 5.42 for the students who attended the class and 6.17 for students who did not attend the class. Without looking at the names of the students, Kelsey randomly selects the college admissions exam scores of students who attended the class and of students who did not attend the class. The results of the samples are provided in the table below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, determine the null and alternative hypotheses for this hypothesis test. Let μ1 be the population mean exam score for students who attended the class and μ2 be the population mean exam score for students who did not attend the class. Attended Class Did Not Attend Class x¯¯¯1=23.74 x¯¯¯2=21.88 n1=32 n2=55 Select the correct answer below: A. Although the population standard deviations are known and the sample sizes are sufficiently large, the samples are not randomly selected and are not independent of each other. B. Although the samples are randomly selected, independent, and sufficiently large, the population standard deviation is not known for both groups. C. Although the population standard deviations are known and the samples are randomly selected and independent, the sample sizes are not sufficiently large. D. All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2<0. E. All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2>0. F. All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2≠0.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Kelsey Matthau is an advisor for a high school. The high school offers a class for students preparing to take college admissions exams. Kelsey is looking for evidence that the population mean score of students who attend the college admissions class is greater than the population mean score of students who do not attend. Since the school has every student take the exam during school hours, Kelsey has access to the students' scores.
Using information from past years, she assumes that the population standard deviation is 5.42 for the students who attended the class and 6.17 for students who did not attend the class. Without looking at the names of the students, Kelsey randomly selects the college admissions exam scores of students who attended the class and of students who did not attend the class.
The results of the samples are provided in the table below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, determine the null and alternative hypotheses for this hypothesis test. Let μ1 be the population mean exam score for students who attended the class and μ2 be the population mean exam score for students who did not attend the class.
| Attended Class | Did Not Attend Class |
|---|---|
| x¯¯¯1=23.74 | x¯¯¯2=21.88 |
| n1=32 | n2=55 |
Select the correct answer below:
A. Although the population standard deviations are known and the sample sizes are sufficiently large, the samples are not randomly selected and are not independent of each other.
B. Although the samples are randomly selected, independent, and sufficiently large, the population standard deviation is not known for both groups.
C. Although the population standard deviations are known and the samples are randomly selected and independent, the sample sizes are not sufficiently large.
D. All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2<0.
E. All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2>0.
F. All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2≠0.
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