P-value in a two-sample z test for the difference of proportions
A medical researcher was curious if the proportion of adult males who are color-blind is the same in the United States and Great Britain. They obtained separate random samples of records for adult men from each country. Here are the sample results: CountryUnited StatesGreat BritainColor-blind\[30\]\[10\]Not\[270\]\[190\]Total\[300\]\[200\] The researcher wants to use these results to test if the proportion of adult men who are color-blind is significantly different in the two countries. They will test \[H_0: p_\text{US} = p_\text{GB}\] versus \[H_a: p_\text{US} \neq p_\text{GB}\]. Assume that all conditions have been met.
0.01 is less than or equal to P is less than 0.05
A political consultant wondered if support for a candidate was significantly different between men and women. The consultant surveyed a random sample of voters. Here are the results: Supports candidate?MenWomenYes\[24\]\[48\]No\[56\]\[52\]Total\[80\]\[100\] The consultant wants to test if these results suggest a significant difference in support between men and women. They will test \[H_0: p_\text{W} = p_\text{M}\] versus \[H_a: p_\text{W} \neq p_\text{M}\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
0.01 is less than or equal to P is less than 0.05
An economist was curious if women were more satisfied with their jobs than men. A random sample of \[220\] workers showed that \[46\] of \[100\] women were satisfied with their jobs, and \[42\] of \[120\] men were satisfied. The economist want to use these results to test \[H_0\text{: }p_\text{W}-p_\text{M}=0\] versus \[H_\text{a}\text{: }p_\text{W}-p_\text{M}>0\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
0.01 is less than or equal to P is less than 0.05
Caroline thinks she can flip a coin so it lands showing heads more often with her right hand. She flipped a coin \[50\] times with each hand. Here the results: ResultRightLeftHeads\[30\]\[20\]Tails\[20\]\[30\]Total\[50\]\[50\] Caroline wants to use these results to test \[H_0\text{: }p_\text{R}-p_\text{L}=0\] versus \[H_\text{a}\text{: }p_\text{R}-p_\text{L}>0\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
0.01 is less than or equal to P is less than 0.05
Joshua plays basketball, and he learned a new technique for shooting free throws. He decided to shoot \[50\] free throws with his old technique and \[50\] with the new technique to see if there was a difference in his performance. He made \[30\] of \[50\] free throws using his old technique, and he made \[38\] of \[50\] using the new technique. He took these shots over multiple days and alternated techniques, so he's willing to assume his data satisfy the conditions for inference. Joshua wants to test if these results suggest a significant difference between the proportions of free throws made with each technique. He will test \[H_0: p_\text{New} = p_\text{Old}\] versus \[H_a: p_\text{New} \neq p_\text{Old}\]. What is the P-value associated with these sample results?
0.05 is less than or equal to P is less than 0.1
Nicki's business ships orders from a location in Chicago and another location in Denver. She suspected that a larger proportion of orders shipped from the Denver location were arriving late. She took a random sample of \[100\] orders from each location. She found that \[20\] orders in the Denver sample arrived late, and \[12\] orders in the Chicago sample arrived late. She wants to use these results to test if the proportion of orders that arrive late is significantly larger at the Denver location. She will test \[H_0: p_\text{Denver} = p_\text{Chicago}\] versus \[H_a: p_\text{Denver} > p_\text{Chicago}\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
0.05 is less than or equal to P is less than 0.1
Researchers suspect that myopia, or nearsightedness, is becoming more common over time. A study from the year \[2000\] showed \[132\] cases of myopia in \[400\] randomly selected people. A separate study from \[2015\] showed \[228\] cases in \[600\] randomly selected people. The researchers want to use these results to test \[H_0\text{: }p_{2015}-p_{2000}=0\] versus \[H_\text{a}\text{: }p_{2015}-p_{2000}>0\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
0.05 is less than or equal to P is less than 0.1
An economist was comparing unemployment rates between states. A random sample of \[800\] adults in Wisconsin showed that \[20\] were unemployed, and a random sample of \[800\] adults in Minnesota showed that \[28\] were unemployed. The economist want to use these results to test \[H_0\text{: }p_\text{MN}-p_\text{WI}=0\] versus \[H_\text{a}\text{: }p_\text{MN}-p_\text{WI}>0\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
0.1 is less than or equal to P is less than 0.15
A large school district was considering changing the start times to its schools. The change would involve high schools starting later and elementary schools starting earlier. The school district was curious if parents supported this change, so they surveyed separate random samples of parents from both types of school in the district. Here are their results: Supports change?High schoolElementaryYes\[54\]\[24\]No\[46\]\[26\]Total\[100\]\[50\] The school district wants to use these results to test if the proportion of parents who support the change is different between these types of schools. They will test \[H_0: p_\text{HS} = p_\text{E}\] versus \[H_a: p_\text{HS} \neq p_\text{E}\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
P is greater than or equal to 0.15
A political consultant wondered if support for a candidate was significantly different between voters who owned a landline telephone and voters who did not. The consultant surveyed a random sample of voters and found \[36\] of \[75\] who owned a landline supported the candidate, while \[27\] of \[100\] who did not own a landline supported the candidate. The consultant wants to test if these results suggest a significant difference in support between voters who do and do not own a landline. They will test \[H_0: p_\text{Landline} = p_\text{No landline}\] versus \[H_a: p_\text{Landline} \neq p_\text{No landline}\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
P is less than 0.01
Researchers studying osteoporosis (bone loss) suspected that women over the age of \[50\] in the United States are diagnosed with the disease more often than women over \[50\] in Mexico. They took a random sample of \[200\] women over the age of \[50\] from each country. Here are the results: Diagnosed with osteoporosis?USMexicoYes\[40\]\[20\]No\[160\]\[180\]Total\[200\]\[200\] The researchers want to use these results to test \[H_0\text{: }p_\text{US}-p_\text{M}=0\] versus \[H_\text{a}\text{: }p_\text{US}-p_\text{M}>0\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
P is less than 0.01
Market researchers wondered if teens were more or less likely than adults to use their mobile phone as an alarm clock. The researchers surveyed a random sample of people and removed those who didn't have a mobile phone. Here are the results: Use phone as alarm?TeenAdultYes\[35\]\[90\]No\[15\]\[60\]Total\[50\]\[150\] The researchers want to test if these results suggest a significant difference between the proportions of teens and adults that use their phone as an alarm clock. They will test \[H_0: p_\text{T} = p_\text{A}\] versus \[H_a: p_\text{T} \neq p_\text{A}\]. Assume that all conditions have been met. What is the P-value associated with these sample results?
The P-value is greater than or equal to 0.15
