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Practice Test - Chapter6, Exams of Statistics

8 Unsolved Problems about Sampling.

Typology: Exams

2021/2022

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Elementary Statistics – Practice Test – Chapter 6
Problems #1 through #3 use the information below.
Suppose that 59% of all people would like to see gun control laws strengthened. In sampling 100
people randomly (with replacement), let x represent the number of people who would like to see gun
control laws strengthened.
1. What is the mean of x in this binomial experiment?
2. What is the standard deviation of x in this binomial experiment?
3. Use the normal approximation of the binomial to compute the probability that x 65.
Solve the following problems.
4. In a random sample of 16,405 babies who were born stillborn, 8,609 were male. Construct a 99%
confidence interval for the proportion of stillborn babies who are male. Source: Annual Statistical
Review, 1956.
5. Using the data from problem #4, what sample size would have been necessary for a two percentage
point error?
6. From a random sample of 51 litters of rats, the mean litter size is 6.11, with an assumed population
standard deviation is 2.27. Construct a 94% confidence interval for the mean litter size of rats
(these values are based on data gathered by King in 1924).
7. Using the data from problem #6, what sample size would have been necessary for a maximum
error of 0.1 rats?
8. Hyoscine is a drug which was once used to improve sleep. In 1908, William Student Gosset (the
developer of Student’s t distribution) studied this drug by measuring amounts of sleep gained by
ten different patients. The mean sleep gained was 2.33 hours, with a standard deviation of 2.00
hours. Assuming that these values are selected from a normal population, construct a 96%
confidence interval for the mean amount of sleep gained by people taking hyoscine.

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Elementary Statistics – Practice Test – Chapter 6

Problems #1 through #3 use the information below.

Suppose that 59% of all people would like to see gun control laws strengthened. In sampling 100 people randomly (with replacement), let x represent the number of people who would like to see gun control laws strengthened.

  1. What is the mean of x in this binomial experiment?
  2. What is the standard deviation of x in this binomial experiment?
  3. Use the normal approximation of the binomial to compute the probability that x ≥ 65.

Solve the following problems.

  1. In a random sample of 16,405 babies who were born stillborn, 8,609 were male. Construct a 99% confidence interval for the proportion of stillborn babies who are male. Source: Annual Statistical Review , 1956.
  2. Using the data from problem #4, what sample size would have been necessary for a two percentage point error?
  3. From a random sample of 51 litters of rats, the mean litter size is 6.11, with an assumed population standard deviation is 2.27. Construct a 94% confidence interval for the mean litter size of rats (these values are based on data gathered by King in 1924).
  4. Using the data from problem #6, what sample size would have been necessary for a maximum error of 0.1 rats?
  5. Hyoscine is a drug which was once used to improve sleep. In 1908, William Student Gosset (the developer of Student’s t distribution) studied this drug by measuring amounts of sleep gained by ten different patients. The mean sleep gained was 2.33 hours, with a standard deviation of 2. hours. Assuming that these values are selected from a normal population, construct a 96% confidence interval for the mean amount of sleep gained by people taking hyoscine.