Unit 7: Inference for Quantitative Data: Means

A one-sample [math]-test is used instead of a [math]-test when:

The degrees of freedom for a one-sample [math]-test with a sample of size [math] is:

The conditions for a one-sample [math]-interval for a mean include:

A paired [math]-test is appropriate when:

As the degrees of freedom increase, the [math]-distribution:

In a two-sample [math]-test for comparing two population means, the null hypothesis is typically:

A confidence interval that does NOT contain zero for [math] suggests:

The test statistic for a one-sample [math]-test is:

When checking the Normal/Large Sample condition for a [math]-test with [math], the most important thing to examine is:

Statistical significance does NOT necessarily mean:

A population has mean μ = 100 and standard deviation σ = 15. For random samples of size n = 25, what is the standard deviation of the sampling distribution of x̄?

If the true population proportion is p = 0.4 and n = 100, what is the standard deviation of the sampling distribution of p̂?

According to the Central Limit Theorem, the sampling distribution of x̄ is approximately normal when:

A statistic is unbiased if:

Two independent populations have means μ₁ = 50 and μ₂ = 45, and standard deviations σ₁ = 6 and σ₂ = 8. For samples of n₁ = 36 and n₂ = 64, what is the standard deviation of x̄₁ − x̄₂?

The sampling distribution of p̂ is approximately normal when:

The mean of the sampling distribution of x̄ equals:

What is the test statistic and conclusion?

What is the 95% confidence interval for the population mean?

What type of test is appropriate and what is the test statistic?

What is the test statistic for comparing the two means?

What conclusion should be drawn at α = 0.05?

What happens to the width of the confidence interval when the sample size increases from 25 to 100?

Which change would increase the power of the test?

For which sample would the t-procedure be most appropriate?

A sample of 25 light bulbs has a mean lifetime of 1200 hours with s = 100 hours. Construct a 95% confidence interval for the true mean lifetime. (t* for df=24 at 95% is 2.064)