In testing the hypothesesH0: μ = 50HA: μ < 50we found that the standardised test statistic is Z = –1.59. Calculate the p-value.Group of answer choices0.02950.05590.11180.9441
Question
In testing the hypothesesH0: μ = 50HA: μ < 50we found that the standardised test statistic is Z = –1.59. Calculate the p-value.Group of answer choices0.02950.05590.11180.9441
Solution
The p-value is calculated by looking up the Z-score in a standard normal distribution table or using a calculator with a normal distribution function.
The Z-score of -1.59 corresponds to a left-tail probability of 0.0561 (or 5.61%). This is the proportion of the distribution that falls to the left of Z = -1.59.
In hypothesis testing, the p-value is the probability of obtaining a result as extreme as, or more extreme than, the observed data, under the assumption that the null hypothesis is true.
Since we are testing the alternative hypothesis HA: μ < 50, we are interested in the left-tail probability. Therefore, the p-value in this case is 0.0561 or 5.61%, which corresponds to the answer choice 0.0559 (rounded to four decimal places).
Similar Questions
In testing the hypothesesH0: μ = 75HA: μ < 75,if the value of the Z test statistic equals -1.78, then the p-value is:Group of answer choices0.9625.0.375.0.5375.0.4625.
Suppose we are testing the hypotheses H0: 𝜇 = 5 versus Ha: 𝜇 > 5, and the conditions for performing the Z test are satisfied. For Z-score = 1.52, calculate the p-value.
A one-sample Z-test with a 2-tailed alternative hypothesis was carried out.A z-statistic of 2.35 has been calculated for the sample mean.Find the P-value, correct to three decimal places.
The rejection region for testing the hypothesesH0: μ = 100HA: μ ≠100at the 0.05 level of significance is:Group of answer choices|Z| > 1.96.Z < 2.33.|Z < 0.95.Z > 1.65.
A significance test was performed to test H0: μ = 2 vs H1: μ ≠ 2 based on a sample of 16 observations.The test statistic is t = −2.125. Based on the Minitab output below, the p-value for this test is in the interval:Group of answer choices(0, 0.01)(0.01, 0.025)(0.025, 0.05)(0.05, 0.1)(0.1, 1)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.