Question

A sample mean, sample size and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 10% significance level. x=27, n=25, =8, Ho =25 Hà #25 The test statistic is z= (Round to two decimal places as needed) Identify the critical value(s) Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed) O A. The critical values are +2/2+ OB. The critical value is za O C . The critical value is -za- ABOU Becom Chegg College the null hypothesis. The data sufficient evidence to conclude that the mean is Corpora Investo Jobs Join Ou

Answer 1

$\\ $ The hypotheses are $ \\ $ Null hypothesis $ H_{o} : \mu = 25 \\ $ Alternate hypothesis $ H_{a} : \mu \neq 25 \\\\ $ Population standard deviation $ (\sigma) = 8 \\\\ $ The sample data is $ \\ $ Sample size $ (n) = 25 \\ $ Sample mean $(\bar{x}) = 27 \\\\ $ Test statistic $ : z = \dfrac{\bar{x} - \mu} { \frac{\sigma}{\sqrt{n}}} = \dfrac{27 - 25}{\frac{8}{\sqrt{25}}} = \textbf{1.25} \\ \\\\ $ As $ H_{a} $ has $ "\neq" $ sign $ , $ so test is 2-tailed $ \\ $ Thus, there are 2 critical values $ \\\\ $ Significance level $ (\alpha) = 10\% = 0.10 \\ $ So, critical values $ : z_{c} = \pm z_{\alpha/2} \\ \hspace*{15 mm}= \pm z_{0.10/2} = \pm z_{0.05} = \mathbf{\pm 1.645}\textbf{ Option A)} \\ ( P( z < -1.64 ) = 0.0505 $ and $ P( z < -1.65) = 0.0495 \\ $ from Z table , so $ P( z < -1.645) $ is closest to 0.05 \\ by extrapolation $)$

$\\ | z | = | 1.25 | = 1.25 \\ | z_{c} | = | \pm 1.645 | = 1.645 \\\\ $ As $ | z | \ngtr | z_{c} | , $ so $ \textbf{Fail to reject} $ the null hypothesis $. $ The data$ \\ \textbf{ does not have} $ sufficient evidence to conclude that the $ \\ $ mean is $ \textbf{different from 25}$