Questions: 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. x̄=29, n=32, σ=9, H0: μ=32, Ha: μ<32 The test statistic is z=-1.89. (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 two decimal places as needed.) A. The critical value is -zα= . B. The critical values are ±zα/2= ± . C. The critical value is zα= .

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.

x̄=29, n=32, σ=9, H0: μ=32, Ha: μ<32

The test statistic is z=-1.89. (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 two decimal places as needed.) A. The critical value is -zα= . B. The critical values are ±zα/2= ± . C. The critical value is zα= .

Transcript text: 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. \[ \bar{x}=29, n=32, \sigma=9, H_{0}: \mu=32, H_{a}: \mu<32 \] The test statistic is $z=-1.89$. (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 two decimal places as needed.) A. The critical value is $-z_{\alpha}=$ $\square$ $\square$. B. The critical values are $\pm z_{\alpha / 2}= \pm$ $\square$ I. C. The critical value is $z_{\alpha}=$ $\square$ .

Solution

Solution Steps

Step 1: Identify the Type of Test

The hypothesis test is a one-tailed test because the alternative hypothesis $ H_a: \mu < 32 $ specifies a direction.

Step 2: Determine the Significance Level

The significance level is given as $ \alpha = 0.10 $.

Step 3: Find the Critical Value

For a one-tailed test at the $ 10\% $ significance level, find the critical value $ z_{\alpha} $ using a standard normal distribution table or calculator.
Since the test is left-tailed, the critical value is $ -z_{\alpha} $.
Look up the critical value for $ \alpha = 0.10 $ in the z-table, which corresponds to the 10th percentile of the standard normal distribution.