Question

il Boost 7:49 PM Exit Question 5 5 pts Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.018; confidence level: 99%;p and unknown 4966 04114 7116 O 5117

Answer 1

Solution:

Question 5)

Solution:

Given,

E = 0.04

c = 99% = 0.99

p and q are unknown . In this case ,

p = 0.5

q = 1 - p = 0.5

Now,

$url=https://latex.codecogs.com/gif.latex?%5Calpha&t=1596240407&ymreqid=f4764063-0d40-e2b0-1cde-f00281012f00&sig=K6NQgcpTjaZFX_nx89zTZg--~D$ = 1 - c = 1 - 0.99 = 0.01

$url=https://latex.codecogs.com/gif.latex?%5Calpha&t=1596240407&ymreqid=f4764063-0d40-e2b0-1cde-f00281012f00&sig=K6NQgcpTjaZFX_nx89zTZg--~D$/2 = 0.005

$url=https://latex.codecogs.com/gif.latex?%5Ctherefore&t=1596240407&ymreqid=f4764063-0d40-e2b0-1cde-f00281012f00&sig=64JCe_IJZ7qxztE0mA_rRg--~D$$url=https://latex.codecogs.com/gif.latex?z_%7B%5Calpha/2%7D&t=1596240407&ymreqid=f4764063-0d40-e2b0-1cde-f00281012f00&sig=nLa9lzRtdgLfe1QOpoG.ZQ--~D$ = 2.576 (using z table)

The sample size for estimating the proportion is given by

n =

/2P(1 - p) E2

= (2.576)² * 0.5 * 0.5 / (0.018²)

= nearly 5117

Answer : 5117

5117

Question:

Claim is "fewer than 16 in 10000"

i.e. p is less than 0.0016

So , null and alternative hypothesis are

H₀ : p = 0.0016

H₁ ; p < 0.0016

O Ho: p = 0.0016 H1: p<0.0016

Question:

The test statistic z is

z =   $url=https://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Chat%20p-p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D&t=1596167392&ymreqid=f4764063-0d40-e2b0-1cde-f0008d012f00&sig=3WpFpTtEmFdUVRm2kKWcfg--~D$ =  (0.30 - 0.25)/$\sqrt{}$[0.25*(1 - 0.25)/696] = 3.05

Answer is

3.05

O 3.05

Question:

For left tailed test ,

p value = P[Z < z][ = P[Z < -1.83] = 0.0336

(use z table to find P[Z < -1.83] )

Since p value is less than alpha level of 0.05 , so we reject the null hypothesis.

So , answer is

0.0336 ; reject the null hypothesis.

0.0336; reject the null hypothesis