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Hypothesis Testing: t-Distribution vs Normal Distribution

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Hypothesis Testing: t-Distribution vs Normal Distribution

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Questions and Answers

What is the effect of substituting the sample standard deviation, S, when the population standard deviation σ is unknown?

It reduces uncertainty

It has no effect

It only affects the sample mean

It introduces extra uncertainty (correct)

What happens when the population standard deviation σ is unknown?

We use the t distribution (correct)

We use the sample mean

We calculate the population mean

We use the normal distribution

Why do we use the t distribution instead of the normal distribution when the population standard deviation σ is unknown?

Because the population standard deviation is unknown (correct)

Because the normal distribution is not suitable for large samples

Because the t distribution is more accurate

Because the sample size is small

What is the reason for not using the normal distribution when the population standard deviation σ is unknown?

The sample standard deviation is used instead (B) Signup and view all the answers

What is the implication of using the sample standard deviation, S, when the population standard deviation σ is unknown?

Extra uncertainty is introduced (D) Signup and view all the answers

What is the primary purpose of a confidence interval in hypothesis testing?

To make inferences about a population parameter (B) Signup and view all the answers

What is the effect of increasing the confidence level on the width of the confidence interval?

The width of the confidence interval increases (B) Signup and view all the answers

What does a 95% confidence interval for a population mean of 10.2 to 12.5 imply?

The true population mean is likely to be between 10.2 and 12.5 (B) Signup and view all the answers

What is the relationship between the margin of error and the width of the confidence interval?

The margin of error is half the width of the confidence interval (D) Signup and view all the answers

What happens to the margin of error as the sample size increases?

The margin of error decreases (A) Signup and view all the answers

What is the effect of increasing the standard deviation of the sample statistic on the margin of error?

The margin of error increases (C) Signup and view all the answers