Which of the following statements are true? When generating confidence intervals

Question

Which of the following statements are true?

When generating confidence intervals and when doing significance tests we use the same expression for the standard error.

If zero is in the confidence interval for the difference between two proportions, we have evidence that the two population proportions could be the same.

When we do a significance test for the difference between two proportions, we're justified in pooling our estimates of the population proportion only if the sample sizes are large.

Question 9 options:

I only

II only

III only

II and III only

I and III only

A company manufactures bolts to be used in missile defense operations. Because of the product’s intended use, the manufacturer needs a 99% confidence interval for the population defect rate. The allowable error is 1%, and the current defect rate is 1%. How many bolts does the manufacturer need to sample to make sure it is meeting its manufacturing standards?

Question 10 options:

Question 11 (4 points)

An AP Statistics student interviewed 100 students (assume SRS) at his school (which has 1100 students) and found that 12 students actually liked the school lunches. Find a 90% confidence interval for the population school lunch approval rate, written from the AP Statistics student’s point of view:

Question 11 options:

Question 12 (4 points)

Last year, 31% of freshman in a large school district listed hip-hop as their favorite type of music. This year, the survey of 500 randomly selected freshmen revealed that 169 listed hip-hop as their favorite type of music. At a 0.01 level of significance, the survey personnel want to know if the proportion of students who preferred hip hop has increased from last year. What z-score would the surveyors calculate?

Question 12 options:

None of the above

Last year, 31% of freshman in a large school district listed hip-hop as their favorite type of music. This year, the survey of 500 randomly selected freshmen revealed that 169 listed hip-hop as their favorite type of music. At a 0.01 level of significance, the survey personnel want to know if the proportion of students who preferred hip hop has increased from last year. What p-value would the surveyors calculate?

Question 13 options:

Question 14 (4 points)

An AP Statistics student interviewed 100 students (assume SRS) at his school (which has 1100 students) and found that 12 students actually liked the school lunches. Find a 99% confidence interval for the population school lunch approval rate, written from the AP Statistics student’s point of view:

Question 14 options:

I only

II only

III only

II and III only

I and III only

A company manufactures bolts to be used in missile defense operations. Because of the product’s intended use, the manufacturer needs a 99% confidence interval for the population defect rate. The allowable error is 1%, and the current defect rate is 1%. How many bolts does the manufacturer need to sample to make sure it is meeting its manufacturing standards?

Question 10 options:

a) 650 b) 659 c) 380 d) 381 e) None of the above

Question 11 (4 points)

An AP Statistics student interviewed 100 students (assume SRS) at his school (which has 1100 students) and found that 12 students actually liked the school lunches. Find a 90% confidence interval for the population school lunch approval rate, written from the AP Statistics student’s point of view:

Question 11 options:

a) I am 90% confident that between 5.3 % and 17.3% of students at our high school like the school lunches. b) I am 90% confident that between 5.3% and 12.3% of students at our high school like the school lunches. c) I am 90% confident that between 6.6% and 12.3% of students at our high school like the school lunches. d) I am 90% confident that between 6.6% and 17.3% of students at our high school like the school lunches. e) None of the above are correct

Question 12 (4 points)

Last year, 31% of freshman in a large school district listed hip-hop as their favorite type of music. This year, the survey of 500 randomly selected freshmen revealed that 169 listed hip-hop as their favorite type of music. At a 0.01 level of significance, the survey personnel want to know if the proportion of students who preferred hip hop has increased from last year. What z-score would the surveyors calculate?

Question 12 options:

a) 1.35 b) 0.0280 c) 0.4278 d) 0.0206 e)

None of the above

Last year, 31% of freshman in a large school district listed hip-hop as their favorite type of music. This year, the survey of 500 randomly selected freshmen revealed that 169 listed hip-hop as their favorite type of music. At a 0.01 level of significance, the survey personnel want to know if the proportion of students who preferred hip hop has increased from last year. What p-value would the surveyors calculate?

Question 13 options:

a) 1.35 b) 0.0885 c) 0.9115 d) 0.0206 e) None of the above Save

Question 14 (4 points)

An AP Statistics student interviewed 100 students (assume SRS) at his school (which has 1100 students) and found that 12 students actually liked the school lunches. Find a 99% confidence interval for the population school lunch approval rate, written from the AP Statistics student’s point of view:

Question 14 options:

a) Between 5.6 % and 18.3% of students at our high school like the school lunches. b) Between 5.3% and 12.3% of students at our high school like the school lunches. c) Between 6.6% and 18.3% of students at our high school like the school lunches. d) Between 6.6% and 17.3% of students at our high school like the school lunches. e) None of the above are correct

Explanation / Answer

Question 11

An AP Statistics student interviewed 100 students (assume SRS) at his school (which has 1100 students) and found that 12 students actually liked the school lunches. Find a 90% confidence interval for the population school lunch approval rate, written from the AP Statistics student’s point of view:

so

n = 100 , 12 students liked it so p = 12/100 = 0.12

so confidence interva of proportion is given as

p +- z*se , where se = sqrt(p*(1-p)/n) = sqrt(0.12*(1-0.12)/100) = 0.0324

and z = 1.645

so 0.12 +- 1.645*0.0324

solving this we get

0.066 ,0.173 , hence 6.6% and 17.3% . so the correct answer is d

quesiton 14

n = 100 , 12 students liked it so p = 12/100 = 0.12

so confidence interva of proportion is given as

p +- z*se , where se = sqrt(p*(1-p)/n) = sqrt(0.12*(1-0.12)/100) = 0.0324

and z = 2.576 , from the z tables

so 0.12 +- 2.576*0.0324

solving this we get

0.036 and 0.203 , hence 3.6% and 20.3% , correct answer is thus e

Please note that we can answer only 1 question at a time , as per the answering guidelines.Have answered 2 for you

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