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Mathematical Statistics (MTMS.01.099, LTMS.00.056 and LTMS.00.057)
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Which of these hypothesis pairs are correctly stated?
The weight of one-month old mice is under study. Population mean is . Let us have the following hypothesis pair
.
Let the actual population mean be . However we end up with a sample of mice whose mean weight is 17g and as a result of our analysis we reject and choose . Therefore we are making:
Let us have sample mean and we have found a confidence interval (8,12) at confidence level 95%. Which of the following statements is correct?
Two confidence intervals were constructed using the same sample - at confidence level 0.95 and at confidence level 0.99. Which of them is wider?
Find the value of the confidence level (1-) .
Find the complement 0.087-quantile of the standard normal distribution.
Write the answer with 2 decimals (e.g. 1.23)
In order to find the confidence interval, one has to know the complement quantile of the standard normal . Find the value of from the figure below.
The sample mean is an unbiased estimate for population mean , because:
Let us have a random sample with the following values 5, 9, 3, 5, 7, 5. Calculate an unbiased estimate for population variance .
Round the answer to 3 decimals (e.g. 1.234).
The graph plots density functions of N(0,1) and t(1) distributions. Which of these corresponds to a standard normal distribution?