an employment information service reports that the mean annual salary for full time male workers ages 25 to 34 with a bachelor's degree is $48718. in a random sample of 12 full time males workers ages 25 to 34 with a bachelor's degree, the mean annual salary is $47164 and the standard deviation is $6500.can you reject the service's claim? use ¦Á =0.05. assume the population is normally distributed.
z = (48718-47164)/(6500/sqrt(12))
z = .828
which one test right-tailed, left
-tailed, or tow-tailed.
To determine if we can reject the employment information service's claim, we need to perform a hypothesis test. Here's how we can proceed:
Step 1: Formulate the hypotheses:
- Null hypothesis (H0): The mean annual salary for full-time male workers ages 25 to 34 with a bachelor's degree is $48718.
- Alternative hypothesis (H1): The mean annual salary for full-time male workers ages 25 to 34 with a bachelor's degree is not $48718.
Step 2: Determine the test statistic:
We'll use the t-test statistic since the sample size is relatively small (<30).
The t-test statistic is calculated using the following formula:
t = (sample mean - population mean) / (sample standard deviation / √n)
Where:
- sample mean = $47164
- population mean = $48718
- sample standard deviation = $6500
- n = sample size = 12
Plugging in the values:
t = ($47164 - $48718) / ($6500 / √12)
Step 3: Calculate the critical value:
Since the population standard deviation is unknown, we'll use the t-table to find the critical value. We are given a significance level of α = 0.05 and degrees of freedom (df) = 11 (n - 1).
Looking up the critical value in the t-table with a two-tailed test and α = 0.05 and df = 11, we find t-critical = ±2.201.
Step 4: Make the decision:
If the calculated t-value falls outside the range of the t-critical values, we reject the null hypothesis; otherwise, we fail to reject it.
Step 5: Calculate the t-value and make the decision:
Plugging the provided values into the formula:
t = (-1554) / (6500 / √12) = -1.419
Since we're performing a two-tailed test, we compare the absolute value of the t-value (-1.419) against the t-critical value (2.201). Since |-1.419| < 2.201, we fail to reject the null hypothesis.
Therefore, based on the given sample data, we do not have enough evidence to reject the service's claim that the mean annual salary for full-time male workers ages 25 to 34 with a bachelor's degree is $48718.