Question

1. A statistics student at a New York State community college, randomly samples 900 students who own cell phones to determine if they play games on their phones. 75% stated that they use their mobile phones to play games.

Using this information, then:

1. construct a 90% confidence interval (to 4 decimal places) for the population proportion, p, of NYS community college cell phone users who play games on their phones.

2. construct a 99% confidence interval (to 4 decimal places) for the population proportion, p, of NYS community college cell phone users who play games on their phones.

3. determine the margin of error for both the 99% and 90% confidence interval estimates.

4. What did you notice about the relationship between the confidence interval width and the margin of error as the confidence interval increased from 90% to 99%?

5. Would it be reasonable for someone to state that 80% of NYS community college cell phone users play games on their cell phones? YOU MUST EXPLAIN YOUR ANSWER OTHERWISE: No credit will be given.

Answer 1

Confielence interval for population proportion p is cakulated as where = sample proportion and ne sample size. Here ² = 75% = 0.75 and n= 900. Å Ita vēci-) (a) for qo% confidence level 221-0.90= 0.10 =) = 0.10 = 0-05 Po = 20.05 = |-645 Hence the confidence interval is 075 0.75 I 1.645* 0.75 * 0.25 900 0.750 1.645 * 0.014434 = 0.750 0.0237 .i lower limit upper limit a = 0,75 -0.0237= 0.7263 - 0.75 +0.0237 0-7737 :. 907. confidence interval is 10-7263, 0.7737) (b 0.005 For 99%. confidence level <=1-0.99-0.01 -)=0 2.576 2 : confidence interval 0.75 † 2.576 * 0.014434 220.005 = 0.75 +0.0372 = 0.75 -0.0372 = 0. 7128 = 0.75 +0.0372 = 0.7872 je Lower limit upper limit Hence 99% confidence interval is (0-7128, 0.7872)

(C) Margin of error *jÔ C1- ) for 90% confidence interved ; margin of error = 1645* 70-75 ¥o-25 = 0.0237 for 99% confidence internal; margin of error = 2:576* 0.75*0-25 qoo 30-0372 = (d). wicth o 90% confidence interval = 0-7737-07263 = 0.0474 cuict the of 99% confidence internal 0.7872-0. 7128 = 0.0744 So som the calculated margin of errors and width of the intervals cue can see that as the confidence level increases margin of error and the width of the interval (which is nothing but 2 * margin of error) also increases. @) we can see from the calculated 90%, and 99% confidence intervals do not contain the value 0-80 liie 80%). Hence, 80% lies outside the confidence interval limite, it is not reasonable for someone to stale that 80% of NYS community college cell phone users play game on their phones.