# Math Help - PLEASE ANSWER? just need some help with a few q's

1. ## PLEASE ANSWER? just need some help with a few q's

my answers so far have been 1 - b, 2 -d, and 3 -a, can someone pls verify?

1) The Central Limit Theorem implies that as the sample size increases, the:

a. sample will approximately follow a normal distribution.
b. middle 95% of data drawn from a sample will approximately follow a normal distribution.
c. sample means drawn from all possible samples will approximately follow a normal distribution.
d. middle 95% of the sampling distribution of the mean will approximately follow a normal distribution.

2) Atmospheric pollution levels in Smogville are recorded (in parts per million) on 25 randomly selected days of the year. This has been repeated for every possible combination of 25 days in a year. The standard error of the mean has been calculated and is equal to 25ppm. If the pollution levels were recorded on 16 (instead of 25) randomly selected days throughout the year, the standard error of the mean would be equal to:

a. 39.0625 ppm
b. 6.25 ppm
c. 7.8125 ppm
d. 31.25 ppm

3) A 90% confidence interval for the mean has been calculated using a sample size of 21. If the sample size is decreased (i.e. n decreases) then, all other things remaining constant, the new confidence interval will be:

a. narrower than the first interval.
b. wider than the first interval.
c. the same as the first interval.
d. a 95% confidence interval.

2. (1) the correct answer is c. Have a play around with this applet, you will see that by increasing the number of samples from a population, then the distribution of the sample means gets closer to normal. http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/

(2) the correct answer is d

(3) the correct answer is b. By looking at the formula for the standard error, you have a division by $\sqrt{n}$. Decreasing n makes $\sqrt{n}$smaller and thus the standard error larger, therefore increasing the width of the confidence interval.

3. Won´t also use of Student´s t-distribution affect the range of the interval?