Question

 An investigator wants to determine if a new program aimed at reducing the overall number of pregnancies in a

highly populated area is effective (reducing average births below 6 per household). In order to carry out the investigation, the investigator conducts a simple random sample of 19 participants in the program and finds the average number of births is 4.7 with a sample standard deviation of 0.9 births. Construct a 95% confidence interval for the average number of births per household in this study. Provide a correct interpretation of your interval.

Parameter of interest

Point estimate

(statistic)

Large samples – all samples are of size 25 or more

Hypothesis testing

CI formulas

Statistic ± (z or t multiplier)*SE

H0 and Ha

Test statistic

Z or t = μ

H0: μ= μ₀ vs

Ha: μ<μ₀, μ μ₀  or μ> μ₀

Z =

p

H0:p = p₀ vs

Ha: p<p₀, p p₀  or p> p₀

Z =      if n > 5

           if n > 5

μ ₁ – μ₂ independent samples

 –

H0: μ ₁ – μ₂ = D₀ vs

Ha: μ ₁ – μ₂ <D₀, μ ₁ – μ₂  D₀ or μ ₁ – μ₂ > D₀ -most times D₀ = 0

Z =

μ _d =μ ₁ – μ₂

matched pairs

D(delta)

H0: μ _d = μ ₁ – μ₂ = D₀ vs

Ha: μ ₁ – μ₂ <D₀, μ ₁ – μ₂  D₀ or μ ₁ – μ₂ > 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

μ

H0: μ= μ₀ vs

Ha: μ<μ₀, μ μ₀  or μ> μ₀

t = , df=n-1

   )

Population of X is

normal

or

symmetric with n between 5 and 10

or

 skewed with n at least 30

p

μ ₁ – μ₂ independent samples

 –

H0: μ ₁ – μ₂ = D₀ vs

Ha: μ ₁ – μ₂ <D₀, μ ₁ – μ₂  D₀ or μ ₁ – μ₂ > D₀ -most times D₀ = 0

t =  with df =  + n₂ -2

and squared   = , where s1 ,s2 are sample standard 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.

μ _d =μ ₁ – μ₂

matched pairs

D(delta)

H0: μ _d = μ ₁ – μ₂ = D₀

Ha: μ ₁ – μ₂ <D₀, μ ₁ – μ₂  D₀ or μ ₁ – μ₂ > D₀ -most times D₀ = 0

Population of deltas is normal

or

symmetric with n between 5 and 10.

or

 skewed with n at least 30.

Hypothesis Testing  CI s and sample size formulas and some definitions

 

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