Question

The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750. a) Develop the appropriate null and alternative hypotheses. b) Assuming the standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the t-statistic

Answer 1

Answer:

The test statistics is   $z = -1$  

Step-by-step explanation:

From the question we are told that

   The sample size is  n  =  100

  The null hypothesis  is  $H_o : \mu = \ 30000$

   The alternative hypothesis is  $H_a : \mu < \ 30000$

   The sample mean is  $\= x = \ 29,750$

    The standard deviation is  $\sigma = \ 2,500$

    The level of significance is  $\alpha =0.05$

Generally the test statistics is mathematically represented as

        $z = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }$

=>      $z = \frac{29750 - 30000 }{ \frac{ 2500}{ \sqrt{100} } }$

=>      $z = -1$