In testing the hypothesesH0: μ = 75.HA: μ < 75,the p-value is found to be 0.042, and the sample mean is 80. Which of the following statements is true?Group of answer choicesNone of the above statements is correct.The probability of observing a sample mean at most as large as 75 from a population whose mean is 100 is 0.042.The probability that the population mean is smaller than 75 is 0.042.The smallest value of α that would lead to the rejection of the null hypothesis is 0.042.
Question
In testing the hypothesesH0: μ = 75.HA: μ < 75,the p-value is found to be 0.042, and the sample mean is 80. Which of the following statements is true?Group of answer choicesNone of the above statements is correct.The probability of observing a sample mean at most as large as 75 from a population whose mean is 100 is 0.042.The probability that the population mean is smaller than 75 is 0.042.The smallest value of α that would lead to the rejection of the null hypothesis is 0.042.
Solution
The correct statement is "The smallest value of α that would lead to the rejection of the null hypothesis is 0.042."
Here's why:
The p-value is the smallest level of significance at which we would reject the null hypothesis. In this case, the p-value is 0.042. This means that if we set our significance level (α) to 0.042, we would just reject the null hypothesis. If α is set to anything larger than 0.042, we would also reject the null hypothesis. Therefore, the smallest value of α that would lead to the rejection of the null hypothesis is 0.042.
The other statements are incorrect. The p-value does not represent the probability that the population mean is smaller than 75, nor does it represent the probability of observing a sample mean at most as large as 75 from a population whose mean is 100.
Similar Questions
Which of the following is a true statement? a. The larger the p-value, the more evidence there is against the null hypothesis. b. The p-value of a test is the probability of getting a test statistic more extreme than the sample result, given that the null hypothesis is true. c. The p-value of a test is the probability of getting a test statistic more extreme than the sample result, given that the null hypothesis is false. d. If the p-value is less than alpha, then the test statistic value is less than the critical value.
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Which of the following facts about the p-value of a test is correct? The larger the p-value, the more evidence the data provide against H0. Regardless of the significance level, a p-value of 0.01 provides enough evidence to reject H0. A p-value smaller than the significance level provides enough evidence to reject H0.
The statement of the alternative hypothesis Ha: μ1 - μ2 < 0, states:Question 5Select one:a.that population mean 1 is smaller than population mean 2.b.that population mean 2 is smaller than population mean 1.c.that population mean 1 is larger than population mean 2.d.that the two population means are the same.
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