If we take a random sample and get a test statistic of zero, what can we conclude? Which of the following statements are true? Select all true statements. Group of answer choicesp-hat = poThe proportion for this sample is equal to the hypothesized value for the proportion in the populationp-hat is 0 standard deviations away from poThe standard error is 0
Question
If we take a random sample and get a test statistic of zero, what can we conclude? Which of the following statements are true? Select all true statements. Group of answer choicesp-hat = poThe proportion for this sample is equal to the hypothesized value for the proportion in the populationp-hat is 0 standard deviations away from poThe standard error is 0
Solution
The following statements are true:
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p-hat = po: This is true because a test statistic of zero indicates that the sample proportion (p-hat) is equal to the hypothesized population proportion (po).
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The proportion for this sample is equal to the hypothesized value for the proportion in the population: This is also true for the same reason as above. The test statistic of zero indicates no difference between the sample proportion and the hypothesized population proportion.
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p-hat is 0 standard deviations away from po: This is true because a test statistic of zero indicates that there is no difference between the sample proportion and the hypothesized population proportion, meaning they are 0 standard deviations apart.
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The standard error is 0: This is not necessarily true. A test statistic of zero does not provide any information about the standard error. The standard error is a measure of the variability of the sample proportion, and it can be zero only if there is no variability in the sample, which is highly unlikely in a random sample.
Similar Questions
If we take a random sample and get a test statistic of zero, what can we conclude? Which of the following statements are true? Select all true statements
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Consider the following competing hypotheses: Ho:μ = 0, HA:μ ≠ 0. The value of the test statistic is z = −1.62. If we choose a 5% significance level, then we __________.Multiple Choicedo not reject the null hypothesis and conclude that the population mean is significantly different from zeroreject the null hypothesis and conclude that the population mean is significantly different from zeroreject the null hypothesis and conclude that the population mean is not significantly different from zerodo not reject the null hypothesis and conclude that the population mean is not significantly different from zero
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