True/False Indicate whether the statement is true or false. Two samples are said
ID: 3207648 • Letter: T
Question
True/False Indicate whether the statement is true or false. Two samples are said to be independent when the selection of the individuals in one sample has no bearing on the selection of those in the other sample. The hypothesis p_1 = p_2 is equivalent to the hypothesis p_1 - p_2 = 0. For n sufficiently large, the distribution of x - mu_x/sigma_x is approximately a standard normal distribution. The standard deviation of the distribution of x decreases as n increases. The confidence interval formula for estimating M when n is large is based on the Central Limit Theorem.Explanation / Answer
Answer:
1.. True (Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.)
2. True (If p1 = p2, then p1 p2 = 0. This is always what goes in the null hypothesis since we start by assuming that the two population means are equal, i.e. the two samples come from the same population)
3.True (The standard normal distribution is a special case of the normal distribution. It is the distribution that occurs when a normal random variable has a mean of zero and a standard deviation of one.
Standard Score (z Score). The normal random variable of a standard normal distribution is called a standard score or a z-score. Every normal random variable X can be transformed into a z score via the following equation:
z = (X - ) /
where X is a normal random variable, is the mean of X, and is the standard deviation of X.
4. True (as the sample size n increases, the variance/standard deviation of the sample mean decreases)
5. True (When the sample size is large, the Central Limit Theorem allows us to calculate confidence intervals for any distribution)
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