Hypothesis Testing for Two Means and Two Proportions Quiz
The question sheet
Reveal any answer as you study-
For two population means from independent samples with unknown population standard deviations, which distribution is used?
- Exponential distribution
- Normal distribution
- Uniform distribution
- Student's t-distribution
Reveal answer
Answer: Student's t-distribution
Source evidence
PDF page 602: Two population means from independent samples where the population standard deviations are not known ̄ ̄
PDF page 602: • Distribution: Student's t-distribution with degrees of freedom (variances not pooled)
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For a hypothesis test of two population proportions from independent samples, which distribution is used?
- Uniform distribution
- Normal distribution
- Chi-square distribution
- Student's t-distribution
Reveal answer
Answer: Normal distribution
Source evidence
PDF page 602: Test of two population proportions from independent samples. ^ ^
PDF page 602: • Distribution: normal distribution
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When testing two population means where population standard deviations are known, which distribution applies?
- Exponential distribution
- Student's t-distribution
- Uniform distribution
- Normal distribution
Reveal answer
Answer: Normal distribution
Source evidence
PDF page 602: A hypothesis test of two population means from independent samples where the population standard deviations are known (typically approximated with the sample standard deviations), will have these characteristics: ̄ ̄
PDF page 602: • Distribution: normal distribution
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In a matched or paired samples t-test, what are the degrees of freedom?
- n – 2
- n – 1
- n
- 2n
Reveal answer
Answer: n – 1
Source evidence
PDF page 602: A hypothesis test for matched or paired samples (t-test) has these characteristics:
PDF page 602: • Distribution: Student’s-t distribution with n – 1 degrees of freedom
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In a matched or paired samples test, the samples are described as:
- Dependent
- Randomized
- Unrelated
- Independent
Reveal answer
Answer: Dependent
Source evidence
PDF page 602: A hypothesis test for matched or paired samples (t-test) has these characteristics:
PDF page 602: • Samples are dependent.
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For two independent means with unknown standard deviations, what is the random variable?
- A single mean
- Mean of the differences
- Pooled proportion
- Difference of the sampling means
Reveal answer
Answer: Difference of the sampling means
Source evidence
PDF page 602: Two population means from independent samples where the population standard deviations are not known ̄ ̄
PDF page 602: • Random Variable: X − X = the difference of the sampling means
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What term means the number of objects in a sample that are free to vary?
- Random variable
- Pooled proportion
- Degrees of freedom
- Standard deviation
Reveal answer
Answer: Degrees of freedom
Source evidence
PDF page 602: Degrees of Freedom (df) the number of objects in a sample that are free to vary. Pooled Proportion estimate of the common value of p1 and p2. Standard Deviation A number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation. Variable (Random Variable) a characteristic of interest in a population being studied. Common notation for variables are upper-case Latin letters X, Y, Z,... Common notation for a specific value from the domain (set of all possible values of a variable) are lower-case Latin letters x, y, z,.... For example, if X is the number of children in a family, then x represents a specific integer 0, 1, 2, 3, .... Variables in statistics differ from variables in intermediate algebra in two following ways.
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For the two-proportions test, the null hypothesis is generally stated as:
- H0: pA ≠ pB
- H0: pA < pB
- H0: pA = pB
- H0: pA > pB
Reveal answer
Answer: H0: pA = pB
Source evidence
PDF page 603: c B A c ⎝n n ⎠ ⎣ B ⎦ A where the null hypothesis is H0: pA = pB or H0: pA – pB = 0. (p′ − p′ )
PDF page 603: B A Test Statistic (z-score): z = 1 ⎞ ⎛ 1 pc(1 − pc) + n ⎠ ⎝n B A where the null hypothesis is H0: pA = pB or H0: pA − pB = 0. where p′A and p′B are the sample proportions, pA and pB are the population proportions, P is the pooled proportion, and n and n are the sample
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In a matched-pairs test, the random variable is:
- Difference of the sample means
- Pooled proportion
- Mean of the differences
- A single proportion
Reveal answer
Answer: Mean of the differences
Source evidence
PDF page 602: A hypothesis test for matched or paired samples (t-test) has these characteristics:
PDF page 602: • Random Variable: x = mean of the differences
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For paired data with fewer than 30 differences, the differences must:
- Follow a normal distribution
- Follow a uniform distribution
- Have equal variances
- Be independent
Reveal answer
Answer: Follow a normal distribution
Source evidence
PDF page 602: • Distribution: Student’s-t distribution with n – 1 degrees of freedom
PDF page 602: • If the number of differences is small (less than 30), the differences must follow a normal distribution.
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For the two-means test with known standard deviations, μ1 – μ2 is generally taken to equal:
- 1
- The sample mean
- 0
- The pooled mean
Reveal answer
Answer: 0
Source evidence
PDF page 603: Generally μ – μ = 0.
PDF page 603: Generally μ1 - μ2 = 0.
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A golf instructor records four students' scores before and after her class. This is:
- A test of two proportions
- A test of two independent means
- A test of a single mean
- A test of matched pairs
Reveal answer
Answer: A test of matched pairs
Source evidence
PDF page 619: 135. A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She
PDF page 619: takes four (4) new students. She records their 18-hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as Table 10.37.
PDF page 604: c. matched or paired samples
Introductory Statistics
Introductory Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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