The professior of a university believes that the average age of the bachelor students is 23. However, the tutor belives that the average age of the bachelor students differs from 23. To test the claim, they randomly selected 100 students, the average age was found to be 24.2 years. Assume the population standard deviation for the student age is 6 years. At the 1% level of significance, what is the test statistics?
Question
The professior of a university believes that the average age of the bachelor students is 23. However, the tutor belives that the average age of the bachelor students differs from 23. To test the claim, they randomly selected 100 students, the average age was found to be 24.2 years. Assume the population standard deviation for the student age is 6 years. At the 1% level of significance, what is the test statistics?
Solution
To find the test statistic, we can use the formula for a z-score in hypothesis testing:
Z = (X - μ) / (σ/√n)
where:
- X is the sample mean
- μ is the population mean
- σ is the population standard deviation
- n is the sample size
In this case:
- X = 24.2 (the sample mean)
- μ = 23 (the population mean)
- σ = 6 (the population standard deviation)
- n = 100 (the sample size)
Substituting these values into the formula, we get:
Z = (24.2 - 23) / (6/√100) = 1.2 / (6/10) = 2
So, the test statistic is 2.
Similar Questions
The ages of students at a university are normally distributed with a mean of 21. What percentage of the student age is at least 21 years old?Question 10Select one:a.21%b.1.96%c.50%d.It could be any value, depending on the magnitude of the standard deviation
A manager of a company believes that the average age of its customers is 40. However, theCEO of the company thinks that the average age of the company’s customers differs from 40. To testthis, she randomly selected 60 customers, and the average customer age was found to be 42.7 years.Assume the (population) standard deviation for customer age is 8 years. Using a 5% level ofsignificance, does the sample provide enough evidence to refute the claim made by the manager
A sample of 39 observations is selected from a normal population. The sample mean is 43, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.02 significance level.
Teacher Joy conducted a census in her class, and she found out that the average time that her students devote to studying is 2.25 hours, their average height is 147 cm, and a random sample of 10 students got an average of 87% in their latest quiz.Which of the given numbers is a statistic?*1 point2.25 Hours147cm87%10 Students
The Marks of 10 students in an English test are given below: 10, 21, 22, 35, 37, 13, 16, 18, 24, 34 What is the population standard deviation of the data?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.