STATISTICS

D P( Z> >​​0.36−0.3​ / ROOT 0.3(0.7) /50

A business knows that 30\%30%30, percent of its customers are less than 252525 years old. The business wants to increase this percentage, so they create a marketing campaign that targets this age group. They want to test H_0:p=0.3H0​:p=0.3H, start subscript, 0, end subscript, colon, p, equals, 0, point, 3 versus H_\text{a}:p > 0.3Ha​:p>0.3H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 3, where ppp is the proportion of this business's customers who are less than 252525 years old after the marketing campaign. After the campaign, the business obtained a random sample of 505050 customers and found that 181818 of those sampled were less than 252525 years old. Which of the following represents the P-value for their test?

C P( ​z<​​0.4−0.45​/ root 0.45(0.55)/500

A campaign manager for a political candidate released a series of advertisements criticizing the opposing candidate in an upcoming election. The opposing candidate previously had the support of 45\%45%45, percent of voters, so the manager wants to test H_0:p=0.45H0​:p=0.45H, start subscript, 0, end subscript, colon, p, equals, 0, point, 45 versus H_\text{a}:p < 0.45Ha​:p<0.45H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 45, where ppp is the proportion of voters that support the opposing candidate. After running the advertisements, the campaign manager obtained a random sample of 500500500 voters and found that 200200200 of those sampled supported the opposing candidate. Which of the following represents the P-value for their test?

P-value≈0.2266

A ketchup company regularly receives large shipments of tomatoes. For quality control purposes, they take a sample of tomatoes from each shipment. If the sample shows convincing evidence that more than 8\%8%8, percent of the tomatoes in the entire shipment are bruised, then the company will request a new shipment of tomatoes. So the company tests H_0: p=0.08H0​:p=0.08H, start subscript, 0, end subscript, colon, p, equals, 0, point, 08 versus H_\text{a}:p>0.08Ha​:p>0.08H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 08, where ppp is the proportion of tomatoes in the entire shipment that are bruised. One day, a supervisor takes a random sample of 600600600 tomatoes from a shipment and finds that 535353 of the tomatoes are bruised, which results in a test statistic of z\approx0.75z≈0.75z, approximately equals, 0, point, 75. Assuming that the necessary conditions are met, what is the approximate P-value associated with the significance test for this shipment?

D P(Z> ​​0.6−0.5​ /ROOT 0.5(0.5) /200

A public opinion survey investigated whether a majority of adults supported a tax increase to help fund the local school system. A random sample of 200200200 adults showed that 120120120 of those sampled supported the tax increase. Researchers want to use these results to test H_0:p=0.5H0​:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus H_\text{a} : p>0.5Ha​:p>0.5H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 5, where ppp is the true proportion of adults that support the tax increase. Which of the following represents the P-value for their test?

P-value = 0.1056

Abdullah is a quality control expert at a factory that paints car parts. He knew that the factory was painting 20\%20%20, percent of the parts with an error, so he made a change in the painting process. After the change, he wanted to test H_0:p=0.2H0​:p=0.2H, start subscript, 0, end subscript, colon, p, equals, 0, point, 2 versus H_\text{a}:p < 0.2Ha​:p<0.2H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 2, where ppp is the proportion of parts that the factory was painting with an error. Abdullah took a sample of 400400400 parts and found that 707070 had an error, and the corresponding test statistic was z=-1.25z=−1.25z, equals, minus, 1, point, 25. Assuming that the necessary conditions are met, what is the approximate P-value for Abdullah's significance test?

P-value≈0.0409

According to a large poll in a previous year, about 80\%80%80, percent of homes in a certain county had access to high-speed internet. The following year, researchers wanted to test H_0: p=0.8H0​:p=0.8H, start subscript, 0, end subscript, colon, p, equals, 0, point, 8 versus H_\text{a}:p<0.8Ha​:p<0.8H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 8, where ppp is the proportion of homes in this county with high-speed internet access. They took a random sample of 250250250 homes from that county and found that 189189189 of them had access to high-speed internet. The test statistic for these results was z\approx -1.74z≈−1.74z, approximately equals, minus, 1, point, 74. Assuming that the necessary conditions are met, what is the approximate P-value for this significance test?

.134

Amanda read a report saying that 49% of teacher in the United States were members of a labor union. She wanted to test whether this was true in her state, so she took a random sample of 300 teachers from her state to test Ho: p = .49 versus Ha: p ≠ .49, where p is the proportion of teachers in her state who are members of a labor union. The sample results showed 134 teachers were members of a labor union, and the corresponding test statistic was z = -1.5. What is the approximate p-value for Amanda's significance test?

C 2⋅P ( ​z< ​​0.43−0.5​/ ROOT 0.5(0.5) /100

Aurelia has a coin that she suspects is unfair. She wants to test H_0:p=0.5H0​:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus H_\text{a}:p \neq 0.5Ha​:p​=0.5H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 5, where ppp is the proportion of flips that this coin lands showing heads. She flipped the coin 100100100 times and it landed showing heads 434343 of those times. Which of the following represents the P-value for Aurelia's test?

P-value ≈0.0588

Ellie read an article claiming that 10\%10%10, percent of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225225225 people from her city to test H_0:p=0.10H0​:p=0.10H, start subscript, 0, end subscript, colon, p, equals, 0, point, 10 versus H_\text{a}:p \neq 0.10Ha​:p​=0.10H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 10, where ppp is the proportion of people in her city that are senior citizens. She found that 313131 of those sampled were senior citizens, and the corresponding test statistic was z \approx 1.89z≈1.89z, approximately equals, 1, point, 89. Assuming that the necessary conditions are met, what is the approximate P-value for Ellie's significance test?

P-value ≈0.0734

Elliot read a report from a previous year saying that 6\%6%6, percent of adults in his city biked to work. He wanted to test whether this had changed, so he took a random sample of 240240240 adults in his city to test H_0:p=0.06H0​:p=0.06H, start subscript, 0, end subscript, colon, p, equals, 0, point, 06 versus H_\text{a}:p \neq 0.06Ha​:p​=0.06H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 06, where ppp is the proportion of adults in Elliot's city that bike to work. The sample results showed 212121 adults who biked to work, and the corresponding test statistic was z \approx 1.79z≈1.79z, approximately equals, 1, point, 79. Assuming that the necessary conditions are met, what is the approximate P-value for Elliot's significance test?

P VALUE 0.0336

Fay read an article that said 26\%26%26, percent of Americans can speak more than one language. She was curious if this figure was higher in her city, so she tested H_0:p=0.26H0​:p=0.26H, start subscript, 0, end subscript, colon, p, equals, 0, point, 26 vs. H_\text{a}:p>0.26Ha​:p>0.26H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 26, where ppp represents the proportion of people in her city that can speak more than one language. She found that 404040 of 120120120 people sampled could speak more than one language. The test statistic for these results was z\approx1.83z≈1.83z, approximately equals, 1, point, 83. Assuming that the necessary conditions are met, what is the approximate P-value for Fay's test?

P-value ≈0.0537

In 2011, 51\%51%51, percent of cell phone owners in a country reported that their cell phone was a smartphone. The following year, the researchers wanted to test H_0: p=0.51H0​:p=0.51H, start subscript, 0, end subscript, colon, p, equals, 0, point, 51 versus H_\text{a}:p>0.51Ha​:p>0.51H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 51, where ppp is the proportion of cell phone owners in that country who have a smartphone. They surveyed a random sample of 934934934 cell phone owners in that country and found that 501501501 of them had a smartphone. The test statistic for these results was z\approx 1.61z≈1.61z, approximately equals, 1, point, 61. Assuming that the necessary conditions are met, what is the approximate P-value for their significance test?

P-value ≈0.0838

The mayor of a town read an article that claimed the national unemployment rate was 8\%8%8, percent. They suspected that the unemployment rate was lower in their town, so they took a sample of 128128128 residents to test H_0: p=0.08H0​:p=0.08H, start subscript, 0, end subscript, colon, p, equals, 0, point, 08 versus H_\text{a}:p<0.08Ha​:p<0.08H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 08, where ppp is the proportion of residents that are unemployed. They found that 666 residents in the sample were unemployed, and the corresponding test statistic was z \approx -1.38z≈−1.38z, approximately equals, minus, 1, point, 38. Assuming that the necessary conditions are met, what is the approximate P-value for this significance test?