When using the central limit theorem for means with n = 98, it is not necessary to assume the distribution of the population data is normally distributed. True False
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When using the central limit theorem for means with n = 98, it is not necessary to assume the distribution of the population data is
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- The Central Limit Theorem says that the standard deviation of the sampling distribution of the sample means is (A exactly equal to the standard deviation. (B close to the population mean if the sample size is small close to the population standard deviation if the sample size is large. equal to the population standard deviation divided by the square root of the sample D size.When taking a sample for research we need to be mindful of the Central Limit Theorem which assumes the population distribution is called?Q2. The sampling distribution of means tends toward Normality only when the underlying populations is Normal. This is true of Central Limit Theorem. TrueB. FalseC. None of the above
- Is it possible for the 50th percentile of a distribution to be equal to the 60th percentile? Why or why not? A. No, because you won’t get the same result multiplying by 50 as you do by 60. B. No, because there will always be some values of the distribution in between the 50th and 60th percentiles. C. Yes, this can happen if the distribution is uniform. D. Yes, this can happen if there are many members of the population with the same value.An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 4 IQ points of the true mean. Assume that σ=10 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.A weight-loss clinic advertised that last month its patients, on average, lost 6 lb. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box. Last month, the number of their clients who lost 6 lb or more was equal to the number of their clients who lost 6 lb or less. Last month at least one of their patients lost exactly 6 lb. Last month at least one of their patients lost less than 10 lb. Two months ago some of their patients lost at least 6 lb. Last month all of their patients lost 6 lb or more. None of the above statements are true. X Ś A 181 Aa ?
- Suppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A n > 30 B The population is normally distributed. C n > 30 OR the population is normally distributed D n > 30 AND the population is normally distributedUse the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 113 pounds and a standard deviation of 37.7 pounds. Random samples of size 20 are drawn from this population and the mean of each sample is determined.Which of the following statements about Chebyshev's theorem is correct? B. Chebyshev's theorem states that all data points lie within three standard deviations of the mean in A. Chebyshev's theorem is only applicable to discrete distributions. any distribution. C. Chebyshev's theorem applies only to positively skewed distributions. D. Chebyshev's theorem applies to any distribution, regardless of its shape. E. Chebyshev's theorem is limited to normal distributions only. F. Chebyshev's theorem guarantees that at least 75% of data lie within three standard deviations of the mean in any distribution. 6. If a data set has a standard deviation of 18 and mean of 70, according to Chebyshev's theorem, what is the interval that must contain at least 19% of the data? A 50 to 90 3 B. 55 to 85 C. 20 to 80 D. 40 to 60 E. 35 to 65 F. None of the above Fina
- It is believed that the mean value of a variable measured for an entire population of individuals has value µ = 17 and that for the population the standard deviation is σ = 5.69. A sample of size n= 43 is to be taken from the population. According to the central limit theorem, the sampling distribution of the mean is Normal( 43 , 0.872 ) Normal( 17 , 5.692 ) Normal( 17 , 0.872 ) Normal( 43 , 5.692 )Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 111 pounds and a standard deviation of 37.8 pounds. Random samples of size 19 are drawn from this population and the mean of each sample is determined. 1₂ = 0 ...Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution, Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is $249 with a standard deviation of $57, Random samples of size 32 are drawn from this population and the mean of each sample is determined. The mean of the distribution of sample means is
