Question

Determine the critical value or values for a one-mean z-test at the 1% significance level if the hypothesis test is right-tailed (Ha:μ>μ0). z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Select the correct answer below: −2.326 −2.054 2.054 2.326 −2.054 and 2.054 −2.326 and 2.326

Answer 1

Answer:

We need to conduct a hypothesis in order to determine if the mean is greater than specified value, the system of hypothesis would be:      

Null hypothesis:$\mu \leq \mu_o$      

Alternative hypothesis:$\mu > \mu_o$      

For this case the significance is 1%. So we need to find a critical value in the normal standard distribution who accumulates 0.99 of the area in the left and 0.01 in the right and for this case this critical value is:

$z_{crit}= 2.326$

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean

$\sigma$ represent the standard deviation for the population      

$n=$ sample size      

$\mu_o$ represent the value that we want to test    

$\alpha$ represent the significance level for the hypothesis test.    

z would represent the statistic (variable of interest)      

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the mean is greater than specified value, the system of hypothesis would be:      

Null hypothesis:$\mu \leq \mu_o$      

Alternative hypothesis:$\mu > \mu_o$      

For this case the significance is 1%. So we need to find a critical value in the normal standard distribution who accumulates 0.99 of the area in the left and 0.01 in the right and for this case this critical value is:

$z_{crit}= 2.326$