Question

After interviewing a sample of 100 residents of New Taipei City, you find that the mean AGE of the sample respondents is 35 years with a standard deviation of 5.0, and that AGE seems fairly normally distributed. However, you are told that the average age of New Taipei City is less than 37 years ten years ago. Based on your sample data, you need to test whether the true average age of all New Taipei City residents is still less than 37 years now. What are the most appropriate null and alternative hypotheses for this test?

Select one:

a. None of the other choices

b. H₀: µ ≥ 37    versus    H₁: µ < 37

c. H₀: µ < 37    versus    H₁: µ ≥ 37

d. H₀: µ = 37    versus    H₁: µ ≠ 37

According to a poll on customer behavior, 30% of people say they will only consider cars manufactured in their country when purchasing a new car. Suppose you select a random sample of 180 respondents. The probability is 80% that the sample percentage will be contained within what symmetrical limits of the population percentage?

Select one:

a. 24.4% and 35.6%

b. 23.3% and 36.7%

c. 25.6% and 34.4%

d. 27.1% and 32.9%

Answer 1

1)

since we are checking if population mean is less than 37 :

Correct option is:

b. H₀: µ ≥ 37    versus    H₁: µ < 37

2)

here population proportion=     μp=	0.3000
sample size       =n=	180

std error of proportion=σp=√(p*(1-p)/n)=0.0342

for middle 80 % values ; crtiical z = -/+ 1.282

therefore  symmetrical limits of the population percentage = 0.3 -/+ 1.28*0.0342 =0.256 to 0.344

~ 25.6 % to 34.4 %

option C is correct