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From OpenStax

Test of a Single Variance Quiz

12 questions math Grades 9-12

The question sheet

Reveal any answer as you study
  1. In the airline delay example, how many flights did the traveler calculate delays for?

    • 150
    • 25
    • 22
    • 15
    Reveal answer

    Answer: 25

    Source evidence

    PDF page 642: Use the following information to answer the next 12 exercises. Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

  2. The airline claims the average delay is at most:

    • 15 minutes
    • 22 minutes
    • 25 minutes
    • 150 minutes
    Reveal answer

    Answer: 15 minutes

    Source evidence

    PDF page 642: Use the following information to answer the next 12 exercises. Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

  3. In the airline example, what was the average delay for the 25 flights?

    • 15 minutes
    • 150 minutes
    • 22 minutes
    • 25 minutes
    Reveal answer

    Answer: 22 minutes

    Source evidence

    PDF page 642: Use the following information to answer the next 12 exercises. Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

  4. A sample standard deviation of 15 minutes equals a sample variance of:

    • 150 minutes
    • 30 minutes
    • 15 minutes
    • 225 minutes
    Reveal answer

    Answer: 225 minutes

    Source evidence

    PDF page 642: 110. A sample standard deviation of 15 minutes is the same as a sample variance of __________ minutes.

    PDF page 642: Use the following information to answer the next 12 exercises. Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

  5. The airline claims the variance of the delay is no more than:

    • 25 minutes
    • 15 minutes
    • 150 minutes
    • 225 minutes
    Reveal answer

    Answer: 150 minutes

    Source evidence

    PDF page 642: Use the following information to answer the next 12 exercises. Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

  6. In the cereal box example, the standard deviation should be at most:

    • 0.5 ounces
    • 84 ounces
    • 15 ounces
    • 0.54 ounces
    Reveal answer

    Answer: 0.5 ounces

    Source evidence

    PDF page 642: 15-ounce cereal boxes it fills has been fluctuating. The standard deviation should be at most 0.5 ounces. To determine if the machine needs to be recalibrated, 84 randomly selected boxes of cereal from the next day’s

  7. How many cereal boxes were weighed to test recalibration?

    • 0.54
    • 15
    • 84
    • 54
    Reveal answer

    Answer: 84

    Source evidence

    PDF page 642: 15-ounce cereal boxes it fills has been fluctuating. The standard deviation should be at most 0.5 ounces. To determine if the machine needs to be recalibrated, 84 randomly selected boxes of cereal from the next day’s

  8. In the cereal box example, the standard deviation of the 84 boxes was:

    • 0.54
    • 0.5
    • 15
    • 84
    Reveal answer

    Answer: 0.54

    Source evidence

    PDF page 643: production were weighed. The standard deviation of the 84 boxes was 0.54. Does the machine need to be recalibrated?

  9. In the store survey, the sample mean price was:

    • $84
    • $43
    • $12
    • $15
    Reveal answer

    Answer: $84

    Source evidence

    PDF page 643: surveying 43 stores, which yielded a sample mean of $84 and a sample standard deviation of $12, test the claim that the standard deviation is greater than $15.

  10. In the store survey, the claim tested is that the standard deviation is greater than:

    • $43
    • $12
    • $84
    • $15
    Reveal answer

    Answer: $15

    Source evidence

    PDF page 643: surveying 43 stores, which yielded a sample mean of $84 and a sample standard deviation of $12, test the claim that the standard deviation is greater than $15.

  11. How many of Isabella's race times were looked up?

    • 57
    • 55
    • 5
    • 3
    Reveal answer

    Answer: 5

    Source evidence

    PDF page 643: mile race is at most 3 minutes. To test her claim, Isabella looks up five of her race times. They are 55 minutes, 61 minutes, 58 minutes, 63 minutes, and 57 minutes.

  12. The airline executive believes the variance of babies is at most:

    • six
    • 3.9
    • nine
    • 18
    Reveal answer

    Answer: nine

    Source evidence

    PDF page 643: adequate safety equipment. They are also interested in the variation of the number of babies. Suppose that an airline executive believes the average number of babies on flights is six with a variance of nine at most. The airline conducts a survey. The results of the 18 flights surveyed give a sample average of 6.4 with a sample standard deviation of 3.9. Conduct a hypothesis test of the airline executive’s belief.

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