1. TRUE or FALSE: Identify which of the following are valid statements and which
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1. TRUE or FALSE: Identify which of the following are valid statements and which ones are false. (a) T F The mean of the t-distribution equals the mean Ho hypothesized under Ho (b) T F All other things being the same, we expect a 95% confidence interval using a standard deviation computed from the sample to be narrower than a 95% confidence interval using a standard deviation assumed to be known from the population c) T F If the distribution of X is skewed, but we take 100 samples of size 10 then, by the CLT, the (d) T F The mean of a population, , is random and hence is considered a random variable. (e) T F The main goal of statistical inference is to generalize information found in the sample to the sampling distribution of is approximately normally distributed. (f) T F Confidence intervals are generally constructed to obtain an estimate for an unknown popu- (g) T F High precision of a confidence interval is associated with low variability of the sampling (h) T F The Standard Normal distribution is preferred over the t-distribution when we need to entire population of interest. lation parameter. distribution of the corresponding sample mean. account for other sources of variability in addition to the variability of the sample mean.Explanation / Answer
a.true .It is important to recognize the the mean for the sampling distribution of the mean is zero when the null hypothesis is true. That's because both populations have the same mean, which also means that both sampling distributions will have the same mean, therefore, the average deviation between the means will be zero.
B. True. 95% confidence means that we used a procedure that works 95% of the time to get this interval. That is, 95% of all intervals produced by the procedure will contain their corresponding parameters. For any one particular interval, the true population percentage is either inside the interval or outside the interval. In this case, it is either in between 350 and 400, or it is not in between 350 and 400. Hence, the probabliity that the population percentage is in between those two exact numbers is either zero or one.
D. False . random variable is the set of possible outcomes mean value cannot be random.
E.true .
Statistical inference is the process of deducing properties of an underlying probability distribution by analysis of data. Inferential statistical analysis infers properties about a population: this includes testing hypotheses and deriving estimates
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