Module 8

Try to match each of the statements written using mathematical notation with their “meaning” finding the statement that matches.

1. The null hypothesis is that the difference between the two true/underlying means is equal to zero

• n = 20

• p₁ > p₂

• x̄ = 12.1

• p₁ = p₂

• H₀: μ₁ – μ₂ = 0

Try to match each of the statements written using mathematical notation with their “meaning” finding the statement that matches.

1. The sample mean is 12.1

• n = 20

• p₁ > p₂

• x̄ = 12.1

• p₁ = p₂

• H₀: μ₁ – μ₂ = 0

Try to match each of the statements written using mathematical notation with their “meaning” finding the statement that matches.

1. The population proportion for the first group is equal to the population proportion for the second group

• n = 20

• p₁ > p₂

• x̄ = 12.1

• p₁ = p₂

• H₀: μ₁ – μ₂ = 0

Try to match each of the statements written using mathematical notation with their “meaning” finding the statement that matches.

1. The sample size is 20

• n = 20

• p₁ > p₂

• x̄ = 12.1

• p₁ = p₂

• H₀: μ₁ – μ₂ = 0

Try to match each of the statements written using mathematical notation with their “meaning” finding the statement that matches.

5. The population proportion for the first group is greater than the population proportion for the second group

• n = 20

• p₁ > p₂

• x̄ = 12.1

• p₁ = p₂

• H₀: μ₁ – μ₂ = 0

Suppose a researcher was originally going to use a sample of 400 to construct a confidence interval, but now only has a budget to use a sample of 100. This means the size of their sample has _____________ (decreased/increased)

Suppose a researcher was originally going to use a sample of 400 to construct a confidence interval, but now only has a budget to use a sample of 100. This means the size of their sample has decreased

This also means that the researcher will have (less/more) data, which means their confidence interval will be (narrower/wider), as it will be harder for them to precisely estimate the parameter of interest.

Select the 2 correct answers from the boxes below

• less

• more

• narrower

• wider

Suppose a researcher was originally going to use a sample of 400 to construct a confidence interval, but now only has a budget to use a sample of 100. This means the size of their sample has decreased.

This also means that the researcher will have less data, which means their confidence interval will be wider, as it will be harder for them to precisely estimate the parameter of interest.

The sample size has changed by a factor of (PART1,two/four) but this change will only affect the width of the confidence interval by a factor of (PART2,four,two) because we model sampling variation for norm-based confidence intervals using the square root of the sample size (the square root of four is two).

Fill both the correct answers for part1 and part2

• PART1 Two

• PART1 Four

• PART2 Two

• PART2 Four

The p-value for this test is _____ (rounded to 4 decimal places).

What is the lower and upper limit of the sample?