Chapter 9 6. Assuming the same level of significance , as the sample size increa
ID: 3309947 • Letter: C
Question
Chapter 9 6. Assuming the same level of significance , as the sample size increases, the value of becomes larger and larger than the value of za/2. 7. When constructing a confidence interval for a sample proportion, the t distribution is appropriate whenever the sample size is small. 8" When the population is normally distributed and the population standard deviation is unknown, then for any sample size n, the sampling distribution of X is based on the t distribution. 9. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample ofn = 100 will be wider than a confidence interval for a population mean based on a sample of n = 50. 10. When the level of confidence and the sample size remain the same, a confidence interval for a population mean will be narrower, when the sample standard deviation s is larger than when s is smaller.Explanation / Answer
Ans:
6)False
When sample size n increases i.e. degree of freedom increases,t distribution more closely represent the normal distribution,so with increasing sample size t and z value becomes approximately same or difference in t and z value decreases.
e.g. For alpha=0.05
when n=10, df=10-1=9
t=TINV(0.05,9)=2.262
when n=30,df=30-1=29
t=TINV(0.05,29)=2.045
z=1.96,which is more closer when n=30.
7)False
We use z distribution for sampling distribution of sample proportions.
8)False
when population standard deviation is unknown and n is small i.e n<30,we use t distribution.
But for larger values of n i.e. n>=30,we can eatimate population standard deviation from sample standard deviation,because for larger n,sampling distribution of sample means is approximately normal(central limit theorm is applicable for n>=30),so we use z distribution for larger values of n.
9)False
As the sample size increases,margin of error decreases(as it isinversely proportional to sqrt(n)),so confidence interval becomes narrower.
So, CI for n=100 will be narrower than CI for n=50
10)False
As,margin of error is directly proportional to standard deviation,so when s is larger,margin of error is larger and CI becomes wider.
Larger the standard deviation,wider the confidence interval.
Smaller the standard deviation,narrower the confidence interval.