Problem
Show Attempt History Current Attempt in Progress * Your answer is incorrect. The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Test $H_{0}: \mu=10$ vs $H_{a}: \mu \neq 10$ when the sample has $n=71, \bar{x}=11.3$, and $s=0.90$ with $S E=0.11$. Find the value of the standardized $z$-test statistic. Round your answer to two decimal places. \[ z=\mathbf{i} 0 \] eTextbook and Media Save for Later Attempts: 1 of 3 used Submit Answer
Solution
Step 1 ：The question is asking for the value of the standardized z-test statistic. The z-test statistic is calculated by subtracting the population mean (μ) from the sample mean (x̄) and dividing by the standard error (SE). The formula for the z-test statistic is: \[ z = \frac{x̄ - μ}{SE} \]
Step 2 ：Given that μ = 10, x̄ = 11.3, and SE = 0.11, we can substitute these values into the formula to find the z-test statistic.
Step 3 ：The calculated z-test statistic is 11.82 when rounded to two decimal places. This value represents how many standard errors the sample mean is away from the population mean.
Step 4 ：Final Answer: The value of the standardized z-test statistic is \(\boxed{11.82}\).
