5. A survey found that 36% of consumers from a Country A are more likely to buy

Question

5. A survey found that 36% of consumers from a Country A are more likely to buy stock in a company based in Country A, or
shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable. Suppose you select a
sample of 200 respondents from Country A. Complete parts (a) through (d) below.

a. What is the probability that in the sample, fewer than 36% are more likely to buy stock in a company based in Country
A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?
The probability is .............. %.
(Round to two decimal places as needed.)

b. What is the probability that in the sample, between 33% and 39% are more likely to buy stock in a company based in
Country A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?
The probability is .............. %.
(Round to two decimal places as needed.)

c. What is the probability that in the sample, more than 33% are more likely to buy stock in a company based in Country
A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?
The probability is............. %.
(Round to two decimal places as needed.)

d. If a sample of 800 is taken, how does this change your answers to (a) through (c)?

If a sample of 800 is taken, what is the probability that in the sample fewer than 36% are more likely to buy stock in a
company based in Country A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more
sustainable?
The probability is............ %.
(Round to two decimal places as needed.)

If a sample of 800 is taken, what is the probability that in the sample between 33% and 39% are more likely to buy stock
in a company based in Country A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming
more sustainable?
The probability is.......... %.
(Round to two decimal places as needed.)

If a sample of 800 is taken, what is the probability that in the sample more than 33% are more likely to buy stock in a
company based in Country A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more
sustainable?
The probability is.............. %.
(Round to two decimal places as needed.)

Explain the how the answers to parts (a) through (c) changed when the sample size was increased to 800.
The answer to part (a) (1)................ the answer to part (b) (2)............... and the answer to part (c)
(3).............. because the probability distribution becomes more (4)................. when the sample size
increases.

(1) increases,
stays the same,
decreases,
(2) increases,
decreases,
stays the same,
(3) decreases
stays the same
increases
(4) skewed
uniform
peaked
symmetric

Explanation / Answer

x= of consumers from a Country A are more likely to buy stock in a company based in Country A, or
shop at its stores,

here we use random variable x binomial distribution with parameter n=200 and p=0.36

SE(p)=sqrt(p(1-p)/n)=sqrt(0.36*(1-0.36)/200)=0.0339

now we use standard normal variate z=(P-p)/SE(p)

(a) for P=0.36, z=(0.36-0.36)/0.0339=0

P(P<0.36)=P(z<0)=0.5

(b) for P=0.33, z=(0.33-0.36)/0.0339=-0.885

for P=0.39,z==(0.39-0.36)/0.0339=0.885

P(0.33<P<0.39)=P(-0.885<z<0.885)=P(z<0.885)-P(z<-0.885)=0.8119-0.1881=0.6238

(c)P(P>0.33)=P(z>-0.885)=1-P(z<-0.885)=1-0.1881=0.8109

(d) here n=800, p=0.36

SE(p)=sqrt(0.36*(1-0.36)/800)=0.017

for P=0.36, z=(0.36-0.36)/0.017=0

P(P<0.36)=P(z<0)=0.5

for P=0.33, z=(0.33-0.36)/0.017=-1.1764

for P=0.39,z=(0.39-0.36)/0.017=-1.1764

P(0.33<P<0.39)=P(-1.1764<z<1.1764)=P(z<1.1764)-P(z<-1.1764)=0.9612-0.0388=0.9224

P(P>0.33)=P(z>-1.1764)=1-P(z<-1.1764)=1-0.0388=0.9612

(last part) Explain the how the answers to parts (a) through (c) changed when the sample size was increased to 800.

bold is right choice

(1) increases,
stays the same,
decreases,
(2) increases,
decreases,
stays the same,
(3) decreases
stays the same
increases
(4) skewed
uniform
peaked
symmetric

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.