1.Current data provided by the 2010 census indicates that the prevalence of breast cancer in the US is still on the rise, while the mortality rates have slightly declined over time. A researcher at a local health department conducts an observational study to determine the prevalence in the particular region. The researcher gathers 2,168 participants and confirms 246 cases of breast cancer in her sample.

A)Assuming the census data indicates a national prevalence of 23.5%, conduct a formal statistical test to determine if the prevalence calculated in the researcher's study differs significantly from the national prevalence levelat the alpha value of 0.05.

B)Interpret your results from the hypothesis test conducted in part A).

Parameter of interest

Point estimate

(statistic)

Large samples - all samples are of size25 or more

Hypothesis testing

CI formulas

Statistic (z or t multiplier)*SE

H0 and Ha

Test statistic

Z or t =

H0: = ₀ vs

Ha: <₀, ₀ or > ₀

Z =

p

H0:p = p₀ vs

Ha: p₀, pp₀ or p> p₀

Z = if n> 5

if n> 5

₁ - ₂ independent samples

-

H0: ₁ - ₂ = D₀ vs

Ha: ₁ - _{2 0}, ₁ - ₂ D₀ or ₁ - ₂ > D₀ -most times D₀ = 0

Z =

_d= ₁ - ₂

matched pairs

D(delta)

H0: _d= ₁ - ₂ = D₀ vs

Ha: ₁ - _{2 0}, ₁ - ₂ D₀ or ₁ - ₂ > D₀ -most times D₀ = 0

Z =

p₁ -p₂

-

H0: p ₁ - p₂ = 0 vs

Ha: p ₁ - p₂ <0,p₁ - p₂ 0 or p₁ - p₂ > 0 -most times D₀ = 0

Z = ,with P=, where x1, x2 are # of successes from samples 1 and 2 respectively.

-

Parameter of interest

Point estimate

Small samples - at least one less than 25

Hypothesis testing

CI formula

Assumptions/conditions

H0: = ₀ vs

Ha: <₀, ₀ or > ₀

t = ,df=n-1

)

Population of Xis

normal

or

symmetric withnbetween 5 and 10

or

skewed with n at least 30

p

₁ - ₂ independent samples

-

H0: ₁ - ₂ = D₀ vs

Ha: ₁ - _{2 0}, ₁ - ₂ D₀ or ₁ - ₂ > D₀ -most times D₀ = 0

t = with df = + n₂ -2

and squared = , where s1 ,s2 are samplestandard deviations of samples 1 and 2 .

-

1.Populations of both X1 and X2 are normal

2.Variances of X1 and X2 are equal

3.X1 and X2 are independent.

_d= ₁ - ₂

matched pairs

D(delta)

H0: _d= ₁ - ₂ = D₀

Ha: ₁ - _{2 0}, ₁ - ₂ D₀ or ₁ - ₂ > D₀ -most times D₀ = 0

Population of deltas is normal

or

symmetric withnbetween 5 and 10.

or

skewed with n at least 30.

Hypothesis Testing CI s and sample size formulas and some definitions