11 Testing a Single Proportion 11.2 Example 12 Testing Two Population Means

11.3 Exercises

1.
Compute $\hat{p}$ for the following situations:
1. (a)
  
  x = 54 and n = 870
2. (b)
  
  x = 327 and n = 641
3. (c)
  
  x = 206 and n = 289
2.
Determine whether the following situations meet both normality criteria or not:
1. (a)
  
  n = 28 and $p_{o}$ = 0.37
2. (b)
  
  n = 540 and $p_{o}$ = 0.80
3. (c)
  
  n = 71 and $p_{o}$ = 0.06
3.
Compute Z for the following situations:
1. (a)
  
  $\hat{p}$ = 0.65, $p_{o}$ = 0.52, n = 78
2. (b)
  
  $\hat{p}$ = 0.11, $p_{o}$ = 0.15, n = 256
3. (c)
  
  $\hat{p}$ = 0.88, $p_{o}$ = 0.85, n = 432
4. (d)
  
  $\hat{p}$ = 0.27, $p_{o}$ = 0.44, n = 157
4.
Compute Z for the following situations:
1. (a)
  
  x = 42, $p_{o}$ = 0.65, n = 60
2. (b)
  
  x = 11, $p_{o}$ = 0.10, n = 187
3. (c)
  
  x = 365, $p_{o}$ = 0.36, n = 1144
4. (d)
  
  x = 204, $p_{o}$ = 0.72, n = 300
5.
Write out $H_{o}$ and $H_{1}$ for the following situations:
1. (a)
  
  We would like to see if the proportion of men who are married has decreased from the reported value of 70% from a few years ago.
2. (b)
  
  In 2012, 55% of eligible voters voted in the presidential election. We would like to see if the proportion of people who plan to vote in the upcoming presidential election will differ from the 55% who voted in 2012.
3. (c)
  
  In 2011, 35% of Americans owned a smartphone. We believe the proportion of Americans who own a smartphone has increased since 2011.
6.
Write out the appropriate hypotheses for the following situations and then test your hypotheses:
1. (a)
  
  You are driving to school when you get stuck waiting for a train. Again. This seems to happen more often than not, and you mention it to your statistics professor. She asks you to keep track of how many times over the next month that you have to wait for a train on your way to school. Out of 25 trips to school, you have to wait for a train 14 times. Do you have to wait for a train more than half the time while driving to school?
2. (b)
  
  In 2009, Microsoft’s Internet Explorer (IE) had 40% of the browser market share. You notice that none of your friends or family uses IE except Grandma. This makes you think that the IE has a market share that is less than 40%, so you decide to conduct a survey to see if IE’s market share has dropped since the end of 2009. After collecting your data, you find that only 63 out of 205 respondents admitted to using Internet Explorer regularly. Has IE’s market share dropped since 2009?
3. (c)
  
  One day while poking around on the Internet, you see a recent poll that claims that 75% of all Americans who have Internet access use Facebook at least once a month. You don’t think this sounds right, so you decide to conduct your own research on the matter to see if the true proportion is different from the claimed value of 75%. You interview 146 people who say they have regular Internet access, and 117 of them say that they check Facebook at least once a month. Is the claim of 75% accurate? Why or why not?