# 10. Introduction to Hypothesis Testing: The z Test Flashcards

Sampling Distribution of z

The distribution of z values that would be obtained if a value of z were calculated for each sample mean for all possible random samples of a given size from some population.

How to convert a raw score into a standard score (z) ?

standard score = (raw score - mean) / standard deviation

How to convert a sample mean to z?

z = [ ̅X - µ(hyp)] / σ(sub ̅X )

z Test for a Population Mean

A hypothesis test that evaluates how far the observed sample mean deviates, in standard error units, from the hypothesized population.

Calculate the value of the z test for the following situation:

̅X = 566

σ = 30

n = 36

µ(hyp) = 560

z = [ ̅X - µ(hyp)] / [σ / √n]

z = (566 - 560) / (30/√5) = 6/5 = 1.2

Calculate the value of the z test for the following situation:

̅X = 24

σ = 4

n = 64

µ(hyp) = 25

z = [ ̅X - µ(hyp)] / [σ / √n]

z = (24 - 25) / (4/√64) = -1 / 0.5 = -2

Calculate the value of the z test for the following situation:

̅X = 82

σ = 14

n = 49

µ(hyp) = 75

z = [ ̅X - µ(hyp)] / [σ / √n]

z = (82 - 75) / (14/√49) = 7 / 2 = 3.5

Calculate the value of the z test for the following situation:

̅X = 136

σ = 15

n = 25

µ(hyp) = 146

z = [ ̅X - µ(hyp)] / [σ / √n]

z = (136 - 146) / (15/√25) = -10 / 3 = -3,33

Null Hypothesis (H0)

A statistical hypothesis that usually asserts that noting special is happening with respect to some characteristic of the underlying population.

Alternative Hypothesis (H1)

The opposite of the null hypothesis.

Research Hypothesis

Usually identified with the alternative hypothesis, this is the informal hypothesis or hunch that inspires the entire investigation.

Indicate what’s wrong with the following statistical hypothesis:

H0 : µ = 155

H1 : µ ≠ 160

Different numbers appear in H0 and H1

Indicate what’s wrong with the following statistical hypothesis:

H0 : ̅X = 241

H1 : ̅X ≠ 241

Sample means (rather than population means) appear in H0 and H1.

First using words, then symbols, identify the null hypothesis for the following situation.

A school administrator wishes to determine whether sixth-grade boys in her school district differ, on average, from the national norms of 10.2 pushups for sixth-grade boys.

Sixth-grade boys in her school district average 10.2 pushups.

H0 : µ = 10.2

First using words, then symbols, identify the null hypothesis for the following situation.

A consumer group investigates whether, on average, the true weights of packages of ground beef sold by a large supermarket chain differ from the specified 16 ounces.

On average, weights of packages of ground beef sold by a large supermarket chain equal 16 ounces.

H0 : µ = 16