Question

. According to Management Accounting, salary figures for certified management accountants (CMAs) who are in the field less than 1 year are normally distributed with a mean of $31,129. A random sample of 15 firstyear CMAs in Denver produces a mean salary of $32,279, with a standard deviation of $1,797. Test the hypothesis that the mean for all Denver firstyear CMAs is not equal to $31,129. Use the .05 level of significance.

Answer 1

The Mean is not equal to $31,129.

Explanation:

Consider the provided information.

The mean is $31129

Thus, the null hypothesis
`H_0: \mu = 31129`

Alternative hypothesis
`H_a: \mu \\eq 31129`

A random sample of 15 firstyear CMAs in Denver produces a mean salary of $32,279, with a standard deviation of $1,797.

Thus the value mean of sample is 32279, standard deviation is 1797 and number of samples are 15.

Now use the 2 sided t-test.

`t=(x-\mu)/((\sigma)/(√(n)))`

Now substitute the respective values in the above formula.

`t=(32279-31129)/((1797)/(√(15)))`

`t=(1150)/(464)`

Test Value = 2.4785 approximately

Now, find the corresponding p-value in your t-table with DF(degree of freedom) 14.

p = 0.0265

as the value of p < 0.05, so you reject null hypothesis.

Thus, the Mean is not equal to $31,129.