A Researcher Collects A Simple Random Sample

Question: ​What’s wrong with the following​ statement?

​”Because the digits​ 0, 1,​ 2, . . .​ , 9 are the normal results from lottery​ drawings, such randomly selected numbers have a normal​ distribution.”

Answer: Since the probability of each digit being selected is​ equal, lottery digits have a uniform​ distribution, not a normal distribution.

Question: What does the notation z alpha ​indicate

Answer: The expression z alpha denotes the z score with an area of alpha to its right.

Question: Which of the following is NOT a descriptor of a normal distribution of a random​ variable?

Answer: The graph is centered around 0.

Question: A continuous random variable has a​ _______ distribution if its values are spread evenly over the range of possibilities.

Answer: A continuous random variable has a uniform distribution if its values are spread evenly over the range of possibilities.

Question: Finding probabilities associated with distributions that are standard normal distributions is equivalent to

Answer: finding the area of the shaded region representing that probability.

Question: Which of the following statistics are unbiased estimators of population​ parameters?

Answer: 1) Sample mean used to estimate a population mean.

2) Sample variance used to estimate a population variance.

3) Sample proportion used to estimate a population proportion.

Question: The sampling distribution of a statistic

Answer: is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.

Question: A researcher collects a simple random sample of​ grade-point averages of statistics​ students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal​ distribution?

Answer: 1) If the population of​ grade-point averages has a normal distribution.

2) The sample has more than 30​ grade-point averages.

Question:

Answer: ​No; the sample means will be normally​ distributed, but the sample of incomes will be skewed to the right.

Question: The Central Limit Theorem

Answer: tells us that for a population with any​ distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.