The followings are the questions I have trouble to answer. I am appreciated your

Question

The followings are the questions I have trouble to answer. I am appreciated your help. May I ask if you provide a step by step explanation, please? Thanks!

1.

A survey claims that 8 out of 10 doctors recommend aspirin for their
patients with headaches. Let p the population proportion of doctors
who recommend aspirin for their patients with headaches. To test
H0 : p = 0.8 vs. Ha : p 6= 0.8, a random sample of 100 doctors’
results in 86 who indicate that they recommend aspirin. Based on the
data set, find the Pvalue of the test.
(a) Pvalue 0.1151
(b) Pvalue 0.2302
(c) Pvalue 0.1336
(d) Pvalue 0.0668

2.

Independent random samples, each containing 800 observations, were
selected from two populations. The samples from populations I and II
produced 320 and 400 successes, respectively. Let p 1 and p 2 denote,
respectively, the true proportions of successes of populations I and II.
Find the pooled estimator for q when q1 = q2 where q1 = 1 p 1 and
q2 = 1 p 2.
(a) 0.55
(b) 0.10
(c) 0.60
(d) 0.60

3.

A sample of size 400 selected from first population has 250 successes,
and a sample of size 200 selected from second population has 150
successes. You are asked to use pooled method for testing the equality
of the two population proportions. Find the observed value of your test
statistic.
(a) 3.2026
(b) 3.0619
(c) 2.8868
(d) 6.4952

A survey claims that 8 out of 10 doctors recommend aspirin for their patients with headaches. Let p the population proportion of doctors who recommend aspirin for their patients with headaches. To test Ho p 0.8 vs. Ha p 0.8, a random sample of 100 doctors results in 86 who indicate that they recommend aspirin. Based on the data set, find the P-value of the test. (a) P-value 0.1151 (b) P-value 0.2302 (c) P-value 0.1336 (d) P-value 0.0668 Independent random samples, each containing 800 observations, were selected from two populations. The samples from populations I and II produced 320 and 400 successes, respectively. Let pi and p2 denote, respectively, the true proportions of successes of populations I and II. Find the pooled estimator for q when q1 q2 where q1 1 and p2 (a) 0.55 (b) 0.10 (c) 0.60 (d) 0.60 A sample of size 400 selected from first population has 250 successes, and a sample of size 200 selected from second population has 150 successes. You are asked to use pooled method for testing the equality of the two population proportions. Find the observed value of your test statistic. (a) -3.2026 (b) -3.0619 (c) -2.8868 (d) -6.4952

Explanation / Answer

Question-1

Sample proportion phat=86/100=0.86

Z-statistic =(phat-0.8)/sqrt(0.8*(1-0.8)/n)

=(0.86-0.8)/ sqrt(0.8*(1-0.8)/100)

=1.5

Two tailed p-value=2*P(Z<-1.5)=2*0.0668=0.1336

So, part-c is answer

Question-2

Pooled estimator of p=(x1+x2)/(n1+n2) = (320+400)/(800+800) =0.45

So, pooled estimator of q=1-0.45=0.55

So part-a is answer

Question-3

Pooled estimator of p=(x1+x2)/(n1+n2) = (250+150)/(400+200) =0.6667

Phat1=250/400=0.625

Phat2=150/200=0.75

Test statistic z= (phat1-phat2)/sqrt(p*(1-p)/(1/n1+1/n2))

=(0.625-0.75)/sqrt(0.6667*(1-0.6667)*(1/400+1/200))

=-3.0619

So, option-b is answer

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