A simple random sample of size n= 40 is obtained from a population that is skewed left with u = 61 and o = 4
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- A simple random sample of size n =66, is obtained from a population that is skewed left with =33 and =3. . Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why?(A) Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. (B) Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. (C)No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x, become approximately normal as the sample size, n, increases. (D) No. The central limit theorem…A simple random sample of size n = 51 is obtained from a population that is skewed left with u = 67 and 0 = 5. Does the population need to be normally distributed for the sampling distribution of x over bar x to be approximately normally distributed? Why? What is the sampling distribution of x overbarx?Ignaz Semmelweiss (1818-1865) was the doctor who first encouraged other doctors to wash their hands with disinfectant before touching patients. Before the new procedure was established, the rate of infection at Dr. Semmelweiss' hospital was about 10%. Afterward the rate dropped to about 1%. Assuming the population proportion of infections was 10%, find the probability that the sample proportion will be 1% or less, assuming a sample size of 200. Start by checking the conditions required for the Central Limit Theorem to apply.
- A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples? (A) The margin of error for S will be 4 times the margin of error for R. (B) The margin of error for S will be 2 times the margin of error for R. (C) The margin of error for S will be equal to the margin of error for R. (D) The margin of error for R will be 4 times the margin of error for S. (E) The margin of error for R will be 2 times the margin of error for S.Let Yn denote the nth order statistic of a random sample of size n froma distribution of the continuous type. Find the smallest value of n for which theinequality P(ξ0.9 < Yn) ≥ 0.75 is true.A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each oftwo random samples selected from the same population: sample R and sample S. Let R represent a random sampleof size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal tothe point estimate obtained from S, which of the following must be true about the respective margins of errorconstructed from those samples?(A) The margin of error for S will be 4 times the margin of error for R.(B) The margin of error for S will be 2 times the margin of error for R.(C) The margin of error for S will be equal to the margin of error for R.(D) The margin of error for R will be 4 times the margin of error for S.(E) The margin of error for R will be 2 times the margin of error for S.
- Find the sampling distributions of Y1 and Yn for ran-dom samples of size n from a continuous uniform popu-lation with α = 0 and β = 1.According to the Central Limit Theorem, the sampling distribution of the mean will be approximately normal whenever n is large. This theorem applies a. To situations in which the sample size is at least 15 b. Regardless of the shape of the population distribution c. Only to populations for which the shape of the distribution is symmetric d. Only to populations for which the random variable is continuous e. All of the above