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

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

Flashcards in 10. Introduction to Hypothesis Testing: The z Test Deck (27)
1
Q

Sampling Distribution of z

A

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.

2
Q

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

A

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

3
Q

How to convert a sample mean to z?

A

z = [ ̅X - µ(hyp)] / σ(sub ̅X )

4
Q

z Test for a Population Mean

A

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

5
Q

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

̅X = 566
σ = 30
n = 36
µ(hyp) = 560

A

z = [ ̅X - µ(hyp)] / [σ / √n]

z = (566 - 560) / (30/√5) = 6/5 = 1.2

6
Q

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

̅X = 24
σ = 4
n = 64
µ(hyp) = 25

A

z = [ ̅X - µ(hyp)] / [σ / √n]

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

7
Q

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

̅X = 82
σ = 14
n = 49
µ(hyp) = 75

A

z = [ ̅X - µ(hyp)] / [σ / √n]

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

8
Q

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

̅X = 136
σ = 15
n = 25
µ(hyp) = 146

A

z = [ ̅X - µ(hyp)] / [σ / √n]

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

9
Q

Null Hypothesis (H0)

A

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

10
Q

Alternative Hypothesis (H1)

A

The opposite of the null hypothesis.

11
Q

Research Hypothesis

A

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

12
Q

Indicate what’s wrong with the following statistical hypothesis:

H0 : µ = 155
H1 : µ ≠ 160

A

Different numbers appear in H0 and H1

13
Q

Indicate what’s wrong with the following statistical hypothesis:

H0 : ̅X = 241
H1 : ̅X ≠ 241

A

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

14
Q

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.

A

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

H0 : µ = 10.2

15
Q

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.

A

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

H0 : µ = 16

16
Q

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

A marriage counselor wishes to determine whether, during a standard conflict-resolution session, his clients differ, on average, from the 11 verbal interruptions reported for “well-adjusted couples”.

A

The marriage counselor’s clients average 11 interruptions per session.

H0 : µ = 11

17
Q

Decision Rule

A

Specifies precisely when H0 should be rejected (because the observed z qualifies as a rare outcome).

18
Q

Critical z Score

A

A z score that separates common from rare outcomes and hence dictates whether H0 should be retained or rejected.

19
Q

Level of Significance (α)

A

The degree of rarity required of an observed outcome in order to reject the null hypothesis (H0).

20
Q

Indicate whether H0 should be retained or rejected and justify your answer by specifying the precise relationship between observed and critical z scores.

Should H0 be retained or rejected, given a hypothesis test with critical z scores of ± 1.96 and…

z = 1.74 ?

A

Retain H0 at the 0.5 level of significance because z = 1.74 is less positive than 1.96.

21
Q

Indicate whether H0 should be retained or rejected and justify your answer by specifying the precise relationship between observed and critical z scores.

Should H0 be retained or rejected, given a hypothesis test with critical z scores of ± 1.96 and…

z = 0.13 ?

A

Retain H0 at the 0.5 level of significance because z = 0.13 is less positive than 1.96.

22
Q

Indicate whether H0 should be retained or rejected and justify your answer by specifying the precise relationship between observed and critical z scores.

Should H0 be retained or rejected, given a hypothesis test with critical z scores of ± 1.96 and…

z = -2.51 ?

A

RejectH0 at the 0.5 level of significance because z = -2.51 is more negative than -1.96.

23
Q

According to the American Psychological Association, members with a doctorate and a full-time teaching appointment earn, on the average, \$82,500 per year, with a standard deviation of \$6,000. An investigator wishes to determine whether \$82,500 is also the mean salary for all female members with a doctorate and a full-time teaching appointment. Salaries are obtained for a random sample of 100 women from this population, and the mean salary equals \$80,100.

Someone claims that the observed difference between \$80,100 and \$82,500 is large enough by itself to support the conclusion that female members earn less than male members. Explain why it is important to conduct a hypothesis test.

A

The observed difference between \$80,100 and \$82,500 cannot be interpreted at face value, as it could have happened just by chance. A hypothesis test permits us to evaluate the effect of chance by measuring the observed difference relative to the standard error of the mean.

24
Q

According to the American Psychological Association, members with a doctorate and a full-time teaching appointment earn, on the average, \$82,500 per year, with a standard deviation of \$6,000. An investigator wishes to determine whether \$82,500 is also the mean salary for all female members with a doctorate and a full-time teaching appointment. Salaries are obtained for a random sample of 100 women from this population, and the mean salary equals \$80,100.

The investigator wishes to conduct a hypothesis test for what population?

A

All female members of the APA with a Ph.D degree and a full-time teaching appointment.

25
Q

According to the American Psychological Association, members with a doctorate and a full-time teaching appointment earn, on the average, \$82,500 per year, with a standard deviation of \$6,000. An investigator wishes to determine whether \$82,500 is also the mean salary for all female members with a doctorate and a full-time teaching appointment. Salaries are obtained for a random sample of 100 women from this population, and the mean salary equals \$80,100.

What is the null hypothesis, H0?

A

H0 : µ = 82,500

26
Q

According to the American Psychological Association, members with a doctorate and a full-time teaching appointment earn, on the average, \$82,500 per year, with a standard deviation of \$6,000. An investigator wishes to determine whether \$82,500 is also the mean salary for all female members with a doctorate and a full-time teaching appointment. Salaries are obtained for a random sample of 100 women from this population, and the mean salary equals \$80,100.

What is the alternative hypothesis, H1?

A

H1 : µ ≠ 82,500

27
Q

According to the American Psychological Association, members with a doctorate and a full-time teaching appointment earn, on the average, \$82,500 per year, with a standard deviation of \$6,000. An investigator wishes to determine whether \$82,500 is also the mean salary for all female members with a doctorate and a full-time teaching appointment. Salaries are obtained for a random sample of 100 women from this population, and the mean salary equals \$80,100.

a) Specify the decision rule, using the 0.5 level of significance.
b) Calculate the value of z.