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It is about ap stats. Chapter 7, Study Guides, Projects, Research of Mathematics

Mathematics

It covers chapter 7 of ap stats it is a study guide

Typology: Study Guides, Projects, Research

2023/2024

Uploaded on 03/28/2024

zoe-hopkins
zoe-hopkins 🇺🇸

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Statistics - Chapter 7 Test
Short Answer
1. A study of college freshmen’s study habits found that the time (in hours) that freshmen use to study each week
follows a distribution with a mean of 7.2 hours and a standard deviation of 5.3 hours.   
(a) What is the shape of the sampling distribution of the mean for samples of 55 randomly selected freshmen?   
Justify your answer.   
(b) What are the mean and standard deviation for the mean number of hours spent studying by an SRS of 55
freshmen?
(c) Find the probability that the average number of hours spent studying by an SRS of 55 students is greater than 9
hours.    Show your work.
.
2. A friend has offered to play a gambling game with you that involves flipping a coin that he has provided.    Since a
flip of heads will be to his advantage, you want to test the coin for fairness before you begin to play.    Your friend
is willing to let you flip the coin 50 times to determine if the probability of getting heads is actually 0.50, as it
should be if the coin is fair.
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Statistics - Chapter 7 Test

Short Answer

  1. A study of college freshmen’s study habits found that the time (in hours) that freshmen use to study each week follows a distribution with a mean of 7.2 hours and a standard deviation of 5.3 hours. (a) What is the shape of the sampling distribution of the mean for samples of 55 randomly selected freshmen? Justify your answer. (b) What are the mean and standard deviation for the mean number of hours spent studying by an SRS of 55 freshmen? (c) Find the probability that the average number of hours spent studying by an SRS of 55 students is greater than 9 hours. Show your work. .
  2. A friend has offered to play a gambling game with you that involves flipping a coin that he has provided. Since a flip of heads will be to his advantage, you want to test the coin for fairness before you begin to play. Your friend is willing to let you flip the coin 50 times to determine if the probability of getting heads is actually 0.50, as it should be if the coin is fair.

(a) Assume for the moment that the coin is fair. If is the proportion of heads in 50 flips of the coin, what are the mean and standard deviation of the sampling distribution of? (b) You flip the coin 50 times and get 30 heads. Do you risk insulting your friend by refusing to play with his coin? Support your answer with an appropriate probability calculation. (Hint: What is the probability of getting a proportion of 0.6 or more?) Be sure to answer the actual question!! .

  1. The weight of the eggs produced by a certain breed of hen is Normally distributed with mean 65 grams (g) and standard deviation 5 g. (a) Calculate the probability that a randomly selected egg weighs between 62.5 g and 68.75 g. Show your work. (b) Think of cartons of such eggs as SRSs of size 12 from the population of all eggs. Calculate the probability that the mean weight of the eggs in a carton falls between 62.5 g and 68.75 g. Show your work. (c) Did you need to know that the population distribution of egg weights was Normal in order to complete parts (a) or (b)? Justify your answer. .
  1. A student investigating study habits asks a simple random sample of 16 students at her school how many minutes they spent on their English homework the previous night. Suppose the actual parameter values for this variable are minutes and minutes. Which of the following best describes what we know about the sampling distribution of means for the student’s sample? A. unknown; shape of distribution unknown B. distribution approximately Normal C. shape of distribution unknown D. distribution approximately Normal E. shape of distribution unknown
  2. In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of the trees show some signs of damage. Which of the following statements is correct? A. 40% is a parameter B. 40% is a statistic C. 40% of all trees in the forest show some signs of damage D. More than 40% of the trees in the forest show some signs of damage E. Less than 40% of the trees in the forest show some signs of damage
  3. The sampling distribution of a statistic is A. the probability that we obtain the statistic in repeated random samples. B. the mechanism that determines whether randomization was effective. C. the distribution of values taken by a statistic in all possible samples of the same sample size from the same population. D. the extent to which the sample results differ systematically from the truth. E. the distribution of values in a sample of size n from the population
  4. A statistic is said to be unbiased if A. the survey used to obtain the statistic was designed so as to avoid even the hint of racial or sexual prejudice. B. the mean of its sampling distribution is equal to the true value of the parameter being estimated. C. both the person who calculated the statistic and the subjects whose responses make up the statistic were truthful. D. the value from any sample is equal to the parameter being estimated. E. it is used for honest purposes only.