17. Doubling the size of the sample will reduce the standard error of the mean t

Question

17. Doubling the size of the sample will

reduce the standard error of the mean to one-half its current value

reduce the standard error of the mean to approximately 70% of its current value

have no effect on the standard error of the mean

double the standard error of the mean

18. A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means
a. whenever the population is infinite
b. whenever the sample size is more than 5% of the population size

c. whenever the sample size is less than 5% of the population size
d. The correction factor is not necessary if the population has a normal distribution

In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. (assuming infinite population)

19. The standard deviation of , known as the standard error of the proportion is approximately

0.5477

5.477

0.05477

54.77

20. Refer to the information in Q19. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is
a. 0.4664
b. 0.9328

c. 0.0336

d. 0.0672

Explanation / Answer

17)reduce the standard error of the mean to approximately 70% of its current value

18)b. whenever the sample size is more than 5% of the population size

19) standard error of the proportion =(p*(1-p)/n)1/2 =(0.4*(1-0.4)/80)1/2 =0.05477

20)

P(0.3<X<0.5)=P((0.3-0.4)/0.05477<Z<(0.5-0.4)/0.05477)=P(-1.8257<Z<1.8257)=0.9664-0.0336 =0.9328

option B

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