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How do you perform a t-test?

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How is hypothesis testing performed using t-tests?

How do you write out Ho and Ha?

What are the options for determining whether a hypothesis test result is significant?

What are critical regions?

How do you determine which t-test is most appropriate to use?

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This solution consists of details of how to perform a t-test.

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Q1. How is hypothesis testing performed using t-tests?
In the following three cases, one needs a t test.
(1) Test if the population mean is different from (or greater than or less than ) a given value when the population standard deviation is unknown.
(2) Test if the two population means are different (or one is greater or smaller ) when the population standard deviations are unknown.
(3) When the samples are dependent.
In the case (1), a one-sample t-test is used, and in the case (2), the independent 2 sample t test will be used, and in the case (3), the paired t-test will be used.

Q2: How do you write out Ho and Ha?
The null hypothesis Ho is a statement of the population parameter(s) that contains an equality ...

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Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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