a recent report claimed that 13 of students typically walk to school

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Lesson 8.3 Checkpoint

11th - 12th grade, mathematics.

12 questions

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Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. Jason chooses an SRS of 60 students and finds that 41 have a computer at home. He would like to carry out a test at the α = 0.05 significance level of H 0 : p = 0.80 versus H a : p < 0.80, where p = the proportion of all students at Jason's high school who have a computer at home. Check if the conditions for performing the significance test are met.

Large Counts? Yes

Random? Yes

Large Counts? fails

Random? SRS of 60 students

Large Counts? np 0 = 60(0.80) = 48 ≥ 10 and n(1-p 0 ) = 60(0.20) = 12 ≥ 10

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 100 students and finds that 17 typically walk to school. DeAnna would like to carry out a test at the α = 0.05 significance level of H 0 : p = 0.13 versus H a : p > 0.13, where p = the proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

Random? Random sample of 100 students

Large Counts? np 0 = 100(0.13) = 13 ≥ 10 and n(1-p 0 ) = 100(0.87) = 87 ≥ 10

A college president says, "More than two-thirds of the alumni support my firing of Coach Boggs." The president's statement is based on 200 emails he has received from alumni in the past three months. The college's athletic director wants to perform a test of H 0 : p = ⅔ versus H a : p > ⅔, where p = the true proportion of the college's alumni who favor firing the coach. Check if the conditions for performing the significance test are met.

Random? No, volunteer response sample

You want to determine if a coin is fair. You toss it 10 times and record the proportion of tosses that land heads. You would like to perform a test of H 0 : p = 0.5 versus H a : p ≠ 0.5, where p = the true proportion of all tosses of the coin that would land heads. Check if the conditions for performing the significance test are met.

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. Jason chooses an SRS of 60 students and finds that 41 have a computer at home. He would like to carry out a test at the α = 0.05 significance level of H 0 : p = 0.80 versus H a : p < 0.80, where p = the proportion of all students at Jason's high school who have a computer at home. Calculate the standardized test statistic.

p̂ = 0.6833

You can't calculate it.

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 100 students and finds that 17 typically walk to school. DeAnna would like to carry out a test at the α = 0.05 significance level of H 0 : p = 0.13 versus H a : p > 0.13, where p = the proportion of all students at her elementary school who typically walk to school. Calculate the standardized test statistic.

A college president says, "More than two-thirds of the alumni support my firing of Coach Boggs." The president's statement is based on 200 emails he has received from alumni in the past three months. The college's athletic director wants to perform a test of H 0 : p = ⅔ versus H a : p > ⅔, where p = the true proportion of the college's alumni who favor firing the coach. Calculate the standardized test statistic.

You want to determine if a coin is fair. You toss it 10 times and record the proportion of tosses that land heads. You would like to perform a test of H 0 : p = 0.5 versus H a : p ≠ 0.5, where p = the true proportion of all tosses of the coin that would land heads. Calculate the standardized test statistic.

p̂ = 0.5733

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. Jason chooses an SRS of 60 students and finds that 41 have a computer at home. He would like to carry out a test at the α = 0.05 significance level of H 0 : p = 0.80 versus H a : p < 0.80, where p = the proportion of all students at Jason's high school who have a computer at home. Find the P-value.

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 100 students and finds that 17 typically walk to school. DeAnna would like to carry out a test at the α = 0.05 significance level of H 0 : p = 0.13 versus H a : p > 0.13, where p = the proportion of all students at her elementary school who typically walk to school. Find the P-value.

Suppose you want to perform a test of H 0 : p = 09.9 versus H a : p > 0.9. An SRS of size 100 from the population of interest yields 96 successes. Find the P-value

Suppose you would like to perform a test of H 0 : p = 0.5 versus H a : p > 0.5. An SRS of size 75 from the population of interest yields 43 successes. Assume that the condition for carrying out the test are met. Find the P-value.

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2. A recent report on elementary schools in Kent county claimed that 13% of elementary students typically walk to school. Trey thinks that the proportion is different than 0.13 at his large elementary school (1000 students). Trey surveys a random sample of 80 students from his school and finds that 17 typically walk to school. Do the data provide convincing evidence that Trey's school has a different proportion of walkers than claimed by the report? Use α = 0.01 STATE: State hypotheses, parameter(s), significance level, and evidence for H₂ Parameter: Statistic: Hypotheses: Significance level: Evidence for H₂:

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A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 100 students and finds that 17 typically walk to school. DeAnna would like to carry out a test at the α=0.05 significance level of H 0 : p = 0.13 versus H a : p > 0.13, where p = the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

Step by Step Answer:

Yes the conditions for performing the significance test are met t... view the full answer.

The Practice Of Statistics

ISBN: 9781319113339

6th Edition

Authors: Daren S. Starnes, Josh Tabor

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