Sampling Distribution and Hypothesis Testing: A Comprehensive Guide with Exercises, Exams of Nursing

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Factors |that |effect |the |sampling |distribution: |- |correct |answer |✔SAMPLE |DESIGN |(SRS): |Non |random |may |be |biased.

SAMPLE |SIZE |(n): |As |becomes |larger, |sample |statistic |converges |on |true |population.

VARIABILTY |(SD): |How |quickly |converges.

Sub-sample |populations |- |correct |answer |✔Used |to |find |out |about |populations.

Sample |statistics |- |correct |answer |✔Used |to |predict |population |parameters.

SEM |(standard |error |of |the |mean) |- |correct |answer |✔One |of |the |most |commonly |reported |measures |of |spread. |Formula: |SEM: |SD/sqrt(n)

Xbar |- |correct |answer |✔SAMPLE |MEAN. |Best |average |of |mean. |Xbar |is |unbiased. |SEM |describes |the |VARIABILITY |of |Xbar. |Regardless |of |the |distribution |of |individuals |in |the |population, |distribution |of |the |sample |mean |(Xbar) |becomes |normal |as |n |gets |large. |in |95% |of |all |samples, |Xbars |lies |within | 2 |SD |of |the |population |mean. |Less |variable |& |more |normal |with |SRS.

Central |Limit |Theorem |- |correct |answer |✔The |theory |allows |us |to |infer |about |mean |from |just | 1 |sample |(using |Xbar, |s). |As |n |within |a |random |sample |becomes |large, |the |sampling |distribution |of |a |statistic |becomes |normal, |even |from |a |strongly |non-normal |population.

Unstandardizing |- |correct |answer |✔Working |with |inverse |normal |distribution.

x= |zs+Xbar

Confidence |Intervals |- |correct |answer |✔A |formal |way |to |make |statements |about |the |probable |location |of |a |parameter |from |a |statistic. |Larger |CI |(smaller |sample)=less |certainty, |SMALLER= |MORE |CERTAINTY. |Typically |use |90% |or |greater. |A |general |formula |to |express |the |confidence |interval |for |the |mean: |(Mean |+/+ |the |standard |error). |(assuming |SD |is |known): |

|Xbar(mean)+/- |Z*(SD/sqrt(n))

What |will |happen |to |the |interval |as |% |confidence |increases? |- |correct |answer

|✔The |interval |will |increase.

Standardizing |- |correct |answer |✔All |normal |curves |are |the |same |if |we |measure |them |in |units |of |size |(SD) |about |the |mean. |A |standardized |value |is |a |"z-score". |

Standard |normal |curve: |mean=0 |& |SD=

(POPULATION): |(x-mean)/SD

(SAMPLE): |z= |(x-xbar)/s

Degrees |of |freedom |- |correct |answer |✔Number |of |samples |minus | 1 |(n-1).

Null |hypothesis |(Ho) |- |correct |answer |✔Test |designed |to |assess |the |strength |of |the |evidence |against |the |null |hypothesis. |A |claim |about |a |population |characteristic |that |is |initially |asummed |to |be |true. |State |in |terms |of |"no |effect" |or |"no |difference". |Will |always |be |an |equality: |(u=uo). |

3 |forms: |u>uo, |u<uo, |u(not)=uo.

|expect |small |test |statistic |and |large |p-value. |Examples: |t-values |(t-tests) |and |F |ratios |(ANOVA).

p-values |- |correct |answer |✔Probability |computed |assuming |that |Ho |is |true |The |LARGER |the |P-value, |the |stronger |evidence |for |null |(FAIL: |TO |REJECT |THE |NULL). |(P>0.05)

The |smaller |the |p-value, |the |stronger |the |evidence |against |Ho |provided |by |the |data |(reject |null). |(P<0.05)

Steps |in |hypothesis |testing: |- |correct |answer |✔1. |State |research |question

2. |State |null |and |alternative |hypothesis
3. |Calculate |the |test |statistic
4. |Report |the |p-value |(range |or |exact)

(when |testing |hyp. |at |specific |a, |this |step |is |diff)

5. |Evaluate |the |assumptions |(normality |"N")
6. |Decision: |reject |or |fail |Ho |based |on |the |p-value
7. |Write |out |interpretation |of |the |result |in |terms |of |initial |scientific |question |(no |statistics)

What |effect |does |increasing |your |sample |size |have |on |t-observed |and |t-critical

|(t)? |- |correct |answer |✔Increases |t-observed |and |decreases |t-critical |(t).

Error |- |correct |answer |✔Only |way |to |be |100% |certain |of |mean |is |to |sample |all |of |the |individuals |in |the |population |of |interest. |There's |always |a |chance |of |error.

Errors |in |hypothesis |testing |- |correct |answer |✔TYPE | 1 |ERROR: |rejecting |Ho |when |Ho |is |true.(a)

TYPE | 2 |ERROR: |failing |to |reject |Ho |when |Ho |is |false. |(B)

a |(alpha) |- |correct |answer |✔Chance |of |a |type | 1 |error, |usually |0.05 |or |5%.

If |P-VALUE>a, |FAIL |TO |REJECT |Ho |(null).

If |p-value |<a, |reject |Ho |(null).

1 |sample |t-test |- |correct |answer |✔Tests |a |hypothesis |about |the |value |of |the |mean |from |a |single |sample |from |population. |Assume |population |is |normally |distributed |with |u/k |mean |and |SD. |(u=uo) |

Degree |of |freedom: |(n-1)

Hyp. |about |the |mean/stand. |error |of |the |mean

Formula:

2 |sample |t-test |- |correct |answer |✔Tests |a |hypothesis |about |the |difference |between | 2 |means |estimated |from | 2 |independent |samples. |Assume |both |populations |are |normally |distributed |with |unknown |mean |and |SD. |(u1=u2) |DF: |n(1)-1 |or |n(2)-1, |whichever |is |smaller.

Hyp. |about |the |means/stand. |error |of |the |means

Formula:

Paired |sample |t-test |- |correct |answer |✔Tests |a |hypothesis |about |the |difference |between | 2 |values |(means) |estimated |from |paired |measurements |on |a |single |sample. |(d=d0) |DF: |n-

d= |the |distance |between | 2 |measures.

Independence |- |correct |answer |✔ 2 |samples |are |independent |if |the |selection |of |individuals |or |objects |that |make |up | 1 |sample |doesn't |influence |the |selection |in |the |other.

Categorical |- |correct |answer |✔Individuals |placed |into |one |or |several |groups.

NOMINAL: |Qualitative |and |unordered |(color)

ORDINAL: |Can |be |ranked |(no, |low, |high)

Quantitative |- |correct |answer |✔Have |values |for |which |arithmetic |operations |make |sense.

CONTINOUS: |any |real |numerical |value |over |an |interval |(foot |length)

DISCRETE: |Finite |number |of |values |(# |of |petals)

Discrete |probability |models: |- |correct |answer |✔SAMPLE |SPACE |(S): |set |of |all |possible |outcomes.

EVENT: |an |outcome |(x) |or |set |of |outcomes.

PROBABILITY |MODEL: |Mathematical |description |consisting |of |sample |space |and |a |way |of |assigning |probabilities |to |events.

Probability |Multiplication |Rule |- |correct |answer |✔If |probabilities |of | 2 |events |are |INDEPENDENT, |you |multiply |them |to |get |total |probability.

Conditional |probability |- |correct |answer |✔When | 2 |events |are |NOT |INDEPENDENT. |Order |is |important. |When |P(A)>0, |the |conditional |probability |of |

B |given |A |is: |P(A+B)/P(A)

Probability |Addition |Rule |- |correct |answer |✔If |A |and |B |are |all |DISJOINT, |then |P(A |or |B): |P(A)+P(B).

Probability |Addition |Rule |- | 2 |events |- |correct |answer |✔P(A)+P(B) |- |P(A |and |B)

If |disjoint |(mutually |exclusive |events), |there |are |no |outcomes |so |probability |= |0.

Probability |Multiplication |Rule |-2 |events |- |correct |answer |✔The |probability |that |both |of |two |events |A |and |B |happen |together |can |be |found |by: |P(A |& |B): |P(A)*P(B/A)

Density |curve |- |correct |answer |✔The |normal |density |curve |describes |the |normal |distribution. |The |total |area |under |the |density |curve |is |exactly |1. |The |curve |is |an |easy |continuous |probability |model.

Probability |Density |Functions |- |correct |answer |✔Meets |the |requirements |of |this |function |when |f(x) |>/0 |for |all |x |between |a |and |b, |and |the |total |area |under |the |curve |between |a |and |b |is |1.0.

Uniform |Probability |Distribution |- |correct |answer |✔AKA |Rectangular |Probability |Distribution. |Describes |f(x): |1/(b-a) |where |a</x</b

Normal |curve |- |correct |answer |✔A |type |of |continuous |probability |distribution. |SYMMETRIC, |SINGLE_PEAKED, |BELL-SHAPED. |Shape |is |described |by |its |mean |and |SD.

Normal |"Gaussian" |curve |- |correct |answer |✔Often |a |good |fit |to |real |data. |Used |as |the |basis |for |statistical |inference.

Parameter |- |correct |answer |✔A |number |that |describes |the |population. |In |statistical |practice, |the |value |of |a |parameter |is |not |known, |because |we |cannot |examine |the |entire |population.

Statistic |- |correct |answer |✔A |number |that |can |be |computed |from |the |sample |data |without |making |use |of |any |unknown |parameters.

Inference |- |correct |answer |✔Provides |methods |for |drawing |conclusions |about |a |population |from |sample |data.

Margin |of |error |- |correct |answer |✔Expressed |certainty |that |your |observed |average |approximates |the |real |average. |z*(SD/sqrt(n))

Standard |Error |- |correct |answer |✔When |the |standard |deviation |of |a |statistic |is |estimated |from |data, |this |is |the |result. |Standard |error |of |sample |mean |(xbar) |is |s/sqrt(n).

Robust |procedures |- |correct |answer |✔Confidence |interval |or |test |when |confidence |level |or |p-value |does |not |change |very |much |when |the |conditions |for |use |of |the |procedure |are |violated.

Significance |tests |- |correct |answer |✔For |Ho |(null |hypothesis). |Based |on |the |t- statistic. |Use |p-values |or |fixed |t- |critical |values.