Question

9 part a) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.17 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains between 12.07 and 12.13 ounces.

A) 0.8475

B) 0.8351

C) 0.1525

D) 0.1649

part b) An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 514 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90% confidence level.

A) 0.63 ± 0.002

B) 0.63 ± 0.035

C) 0.37 ± 0.002

D) 0.37 ± 0.035

  part c) Find the standardized test statistic, z, to test the hypothesis that p1 < p2. Use α = 0.10. The sample statistics listed below are from independent samples. Sample statistics: n1 = 550, x1 = 121, and n2 = 690, x2 = 195

A) 1.116

B) -2.513

C) -2.132

D) -0.985

part d) The mean monthly gasoline bill for one household is greater than $150. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to support the claim μ > $150.

B) There is sufficient evidence to support the claim μ > $150.

C) There is not sufficient evidence to reject the claim μ > $150.

D) There is sufficient evidence to reject the claim μ > $150

Answer 1

a)

probability =P(12.07<X<12.13)=P((12.07-12.17)/0.04)<Z<(12.13-12.17)/0.04)=P(-2.5<Z<-1)=0.1587-0.0062=0.1525

b)

sample size          n=	514
sample proportion p̂ =x/n=	0.3700
std error se= √(p*(1-p)/n) =	0.0213
for 90 % CI value of z=	1.645
margin of error E=z*std error   =	0.035

option D is correct

c)

B) -2.513

d)

A) There is not sufficient evidence to support the claim μ > $150.