Central Limit Theorem (Cookie Recipes) Quiz

PDF page 443: X = length of time (in days) that a cookie recipe lasted at the Olmstead Homestead. (Assume that each of the different recipes makes the same quantity of cookies.)

PDF page 443: • The student will demonstrate and compare properties of the central limit theorem.

PDF page 443: Use a random number generator to randomly select four samples of size n = 5 from the given population. Record your samples in Table 7.5. Then, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.

PDF page 443: Use a random number generator to randomly select four samples of size n = 5 from the given population. Record your samples in Table 7.5. Then, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.

PDF page 444: samples of size n = 10. Record the samples in Table 7.6. As before, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.

PDF page 447: n sample is sufficiently large, then the distribution of the sample means and the distribution of the sample sums will approximate a normal distribution regardless of the shape of the population. The mean of the sample means will equal the population mean, and the mean of the sample sums will equal n times the population mean. The standard σ deviation of the distribution of the sample means, , is called the standard error of the mean n

PDF page 447: In a population whose distribution may be known or unknown, if the size (n) of the sample is sufficiently large, the distribution of the sample means will be approximately normal. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, called the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (n).

PDF page 447: In a population whose distribution may be known or unknown, if the size (n) of the sample is sufficiently large, the distribution of the sample means will be approximately normal. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, called the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (n).

PDF page 447: sampling distribution given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. σ standard error of the mean the standard deviation of the distribution of the sample means, or n

PDF page 448: The central limit theorem tells us that for a population with any distribution, the distribution of the sums for the sample means approaches a normal distribution as the sample size increases. In other words, if the sample size is large enough, the distribution of the sums can be approximated by a normal distribution, even if the original population is not normally distributed. Additionally, if the original population has a mean of μX and a standard deviation of σx, the mean of the sums is

PDF page 448: Mean for sums (∑X): (n)(μx)

PDF page 448: nμx and the standard deviation is ( n) (σx), where n is the sample size.

PDF page 448: Standard deviation for sums (∑X): ( n) (σx)

PDF page 448: The central limit theorem can be used to illustrate the law of large numbers. The law of large numbers states that the larger ̄ the sample size you take from a population, the closer the sample mean, x , gets to μ.

PDF page 448: Use the following information to answer the next six exercises: Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let Χ be the random variable representing the time ̄ it takes her to complete one review. Assume Χ is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.

PDF page 461: 1 mean = 4 hours, standard deviation = 1.2 hours, sample size = 16

PDF page 448: Use the following information to answer the next six exercises: Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let Χ be the random variable representing the time ̄ it takes her to complete one review. Assume Χ is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.

PDF page 461: 1 mean = 4 hours, standard deviation = 1.2 hours, sample size = 16